Find GCF and LCM - 6th Grade Math

1. What is the GCF of $35$ and $49$?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

9. What is the LCM of $5$ and $12$?

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

10. What is the GCF of $60$ and $84$?

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

11. What is the GCF of $75$ and $100$?

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

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

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

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

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

14. What is the LCM of $4$ and $9$?

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

15. What is the LCM of $4$ and $6$?

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

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

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

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

    $7$. Since $35 = 5 \times 7$ and $49 = 7 \times 7$, GCF is $7$.

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

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

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

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

20. What is the LCM of $8$ and $12$?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

30. What is the GCF of $45$ and $100$?

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

31. What is the prime factorization of $84$?

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

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

    $32$. Since $64 = 2^6$ and $96 = 2^5 \times 3$, GCF is $2^5 = 32$.

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

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

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

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

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

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

36. What is the LCM of $6$ and $8$?

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

37. What is the GCF of $48$ and $72$?

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

38. What is the prime factorization of $60$?

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

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

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

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

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

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

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

42. What is the GCF of $48$ and $60$?

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

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

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

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

    $42$. Since $6$ and $7$ are coprime, LCM = $6 \times 7$.

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

    $60$. Since $5$ and $12$ share no factors, LCM = $5 \times 12$.

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

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

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

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

48. What is the GCF of $28$ and $42$?

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

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

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

50. What is the LCM of $9$ and $12$?

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

51. What is the LCM of $7$ and $12$?

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

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

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

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

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

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

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

55. What is the LCM of $10$ and $12$?

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

56. What is the GCF of $36$ and $54$?

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

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

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

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