6th Grade Math Flashcards: Find Gcf And Lcm

What this deck covers

This deck focuses on Find Gcf And Lcm, giving you a quick way to review the definitions, rules, and examples that matter most for 6th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the GCF of $35$ and $49$?

Answer: $7$. $35 = 5 \times 7$ and $49 = 7^2$ share only $7$.

Flashcard 2: What is the distributive property for factoring a common factor from a sum?

Answer: $ab + ac = a(b + c)$. Factor out the common term $a$ from both addends.

Flashcard 3: What is the GCF of $32$ and $24$, and write $32+24$ as a product?

Answer: $8(4+3)$. GCF is $8$; $32+24=56=8(4+3)$.

Flashcard 4: What is the least common multiple (LCM) of $8$ and $12$?

Answer: $24$. Find the smallest multiple shared by $8$ and $12$.

Flashcard 5: What expression factors $36+8$ using the GCF and leaves no common factor inside parentheses?

Answer: $4(9+2)$. GCF of $36$ and $8$ is $4$; $36÷4=9$, $8÷4=2$.

Flashcard 6: What is the greatest common factor (GCF) of $81$ and $63$?

Answer: $9$. Both $81$ and $63$ are divisible by $9$ with no larger common factor.

Flashcard 7: What is the least common multiple (LCM) of $a$ and $b$?

Answer: The smallest positive whole number that is a multiple of both $a$ and $b$. The LCM is the smallest number divisible by both.

Flashcard 8: What is the least common multiple (LCM) of $10$ and $12$?

Answer: $60$. The smallest number that both $10$ and $12$ divide into.

Flashcard 9: What is the LCM of $5$ and $12$?

Answer: $60$. Multiples of $5$: $5,10,15,...,60$; of $12$: $12,24,36,48,60$.

Flashcard 10: What is the GCF of $60$ and $84$?

Answer: $12$. Common prime factors: $2^2 \times 3 = 12$.

Flashcard 11: What is the GCF of $75$ and $100$?

Answer: $25$. Common factors: $5^2 = 25$.

Flashcard 12: What is $56 + 14$ written as a product using the GCF?

Answer: $14(4 + 1)$. GCF of $56$ and $14$ is $14$; $56 = 14 \times 4$, $14 = 14 \times 1$.

Flashcard 13: What is $27 + 18$ written as a product using the GCF?

Answer: $9(3 + 2)$. GCF of $27$ and $18$ is $9$; $27 = 9 \times 3$, $18 = 9 \times 2$.

Flashcard 14: What is the LCM of $4$ and $9$?

Answer: $36$. $4$ and $9$ share no common factors, so LCM = $4 \times 9 = 36$.

Flashcard 15: What is the LCM of $4$ and $6$?

Answer: $12$. Multiples of $4$: $4,8,12$; of $6$: $6,12$.

Flashcard 16: What is the GCF of $45$ and $30$, and write $45+30$ as a product?

Answer: $15(3+2)$. GCF is $15$; $45+30=75=15(3+2)$.

Flashcard 17: What is the greatest common factor (GCF) of $35$ and $49$?

Answer: $7$. Since $35 = 5 imes 7$ and $49 = 7 imes 7$, GCF is $7$.

Flashcard 18: What expression factors $48+18$ using the GCF and leaves no common factor inside parentheses?

Answer: $6(8+3)$. GCF of $48$ and $18$ is $6$; factor it out completely.

Flashcard 19: What is the distributive property for expanding a factored expression?

Answer: $a(b + c) = ab + ac$. Multiply $a$ by each term inside the parentheses.

Flashcard 20: What is the LCM of $8$ and $12$?

Answer: $24$. Multiples of $8$: $8,16,24$; of $12$: $12,24$.

Flashcard 21: What is the distributive property pattern for factoring a common factor: $ab+ac$?

Answer: $ab+ac=a(b+c)$. Factor out the common term $a$ from both addends.

Flashcard 22: What is $45 + 30$ written as a product using the GCF?

Answer: $15(3 + 2)$. GCF of $45$ and $30$ is $15$; $45 = 15 \times 3$, $30 = 15 \times 2$.

Flashcard 23: What is the greatest common factor (GCF) of $a$ and $b$?

Answer: The greatest whole number that divides both $a$ and $b$. The GCF is the largest factor shared by both numbers.

Flashcard 24: What is the least common multiple (LCM) of two whole numbers?

Answer: The smallest positive multiple that both numbers share. It's the smallest number that both numbers divide into evenly.

Flashcard 25: What expression factors $28+56$ using the GCF and leaves no common factor inside parentheses?

Answer: $28(1+2)$. GCF of $28$ and $56$ is $28$; $56÷28=2$.

Flashcard 26: What is the least common multiple (LCM) of $4$ and $6$?

Answer: $12$. The smallest number divisible by both $4$ and $6$.

Flashcard 27: What is the greatest common factor (GCF) of $45$ and $60$?

Answer: $15$. The largest factor shared by both $45$ and $60$.

Flashcard 28: What expression factors $63+42$ using the GCF and leaves no common factor inside parentheses?

Answer: $21(3+2)$. Factor out GCF $21$ from both terms.

Flashcard 29: What is the greatest common factor (GCF) of $24$ and $36$?

Answer: $12$. Find the largest number that divides both $24$ and $36$ evenly.

Flashcard 30: What is the GCF of $45$ and $100$?

Answer: $5$. $45 = 3^2 \times 5$ and $100 = 2^2 \times 5^2$ share only $5$.

Flashcard 31: What is the prime factorization of $84$?

Answer: $2^2 \cdot 3 \cdot 7$. $84 = 4 \times 21 = 4 \times 3 \times 7 = 2^2 \times 3 \times 7$.

Flashcard 32: What is the greatest common factor (GCF) of $64$ and $96$?

Answer: $32$. Since $64 = 2^6$ and $96 = 2^5 imes 3$, GCF is $2^5 = 32$.

Flashcard 33: What is the greatest common factor (GCF) of two whole numbers?

Answer: The greatest whole number that divides both numbers evenly. It's the largest factor that both numbers have in common.

Flashcard 34: What is the distributive property pattern for expanding: $a(b+c)$?

Answer: $a(b+c)=ab+ac$. Multiply $a$ by each term inside the parentheses.

Flashcard 35: What is the least common multiple (LCM) of $9$ and $12$?

Answer: $36$. The first common multiple of $9$ and $12$ is $36$.

Flashcard 36: What is the LCM of $6$ and $8$?

Answer: $24$. Multiples of $6$: $6, 12, 18, 24$; multiples of $8$: $8, 16, 24$.

Flashcard 37: What is the GCF of $48$ and $72$?

Answer: $24$. Common factors: $48 = 2^4 \times 3$, $72 = 2^3 \times 3^2$; GCF = $2^3 \times 3 = 24$.

Flashcard 38: What is the prime factorization of $60$?

Answer: $2^2 \cdot 3 \cdot 5$. $60 = 4 \times 3 \times 5 = 2^2 \times 3 \times 5$.

Flashcard 39: What is $24 + 60$ written as a product using the GCF?

Answer: $12(2 + 5)$. GCF of $24$ and $60$ is $12$; $24 = 12 \times 2$, $60 = 12 \times 5$.

Flashcard 40: What is $63 + 42$ written as a product using the GCF?

Answer: $21(3 + 2)$. GCF of $63$ and $42$ is $21$; $63 = 21 \times 3$, $42 = 21 \times 2$.

Flashcard 41: What is the GCF of $63$ and $21$, and write $63+21$ as a product?

Answer: $21(3+1)$. GCF is $21$; $63+21=84=21(3+1)$.

Flashcard 42: What is the GCF of $48$ and $60$?

Answer: $12$. Common factors: $2^2 \times 3 = 12$.

Flashcard 43: What is the GCF of $56$ and $14$, and write $56+14$ as a product?

Answer: $14(4+1)$. GCF is $14$; $56+14=70=14(4+1)$.

Flashcard 44: What is the least common multiple (LCM) of $6$ and $7$?

Answer: $42$. Since $6$ and $7$ are coprime, LCM = $6 imes 7$.

Flashcard 45: What is the least common multiple (LCM) of $5$ and $12$?

Answer: $60$. Since $5$ and $12$ share no factors, LCM = $5 imes 12$.

Flashcard 46: What is the distributive property used for factoring: $ab+ac=\,?$

Answer: $a(b+c)$. Factor out the common term $a$ from both terms.

Flashcard 47: What is $36 + 8$ written as a product using the GCF?

Answer: $4(9 + 2)$. GCF of $36$ and $8$ is $4$; $36 = 4 \times 9$, $8 = 4 \times 2$.

Flashcard 48: What is the GCF of $28$ and $42$?

Answer: $14$. Common factors: $2 \times 7 = 14$.

Flashcard 49: What is the greatest common factor (GCF) of $54$ and $72$?

Answer: $18$. Both numbers share $18$ as their highest common divisor.

Flashcard 50: What is the LCM of $9$ and $12$?

Answer: $36$. Multiples of $9$: $9,18,27,36$; of $12$: $12,24,36$.

Flashcard 51: What is the LCM of $7$ and $12$?

Answer: $84$. $7$ and $12$ share no common factors, so LCM = $7 \times 12 = 84$.

Flashcard 52: What is the GCF of $81$ and $27$, and write $81+27$ as a product?

Answer: $27(3+1)$. GCF is $27$; $81+27=108=27(3+1)$.

Flashcard 53: What expression factors $90+75$ using the GCF and leaves no common factor inside parentheses?

Answer: $15(6+5)$. GCF of $90$ and $75$ is $15$; divide to get the factors.

Flashcard 54: What expression factors $84+30$ using the GCF and leaves no common factor inside parentheses?

Answer: $6(14+5)$. GCF of $84$ and $30$ is $6$; factor completely.

Flashcard 55: What is the LCM of $10$ and $12$?

Answer: $60$. LCM = $\frac{10 \times 12}{\text{GCF}(10,12)} = \frac{120}{2} = 60$

Flashcard 56: What is the GCF of $36$ and $54$?

Answer: $18$. Common factors: $2 \times 3^2 = 18$.

Flashcard 57: What is the GCF of $36$ and $8$, and factor $36+8$ using it?

Answer: $4(9+2)$. GCF is $4$; $36+8=44=4(9+2)$.