Least Common Multiple

Help Questions

ACT Math › Least Common Multiple

Questions 1 - 10

A sliced cake can be equally split among 4, 5, or 6 people, with each person receiving the same number of slices. Which of the following answers represents a possible number of slices that the cake could have?

116

120

Explanation

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

116

120

Explanation

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

What is the least common multiple of 8, 25, and 40?

$200$

$160$

$125$

$120$

$400$

Explanation

Find the multiples of 40, and find the smallest one that is divisible by 8 and 25.

What is the least common multiple of 8, 25, and 40?

$200$

$160$

$125$

$120$

$400$

Explanation

Find the multiples of 40, and find the smallest one that is divisible by 8 and 25.

What is the least common multiple of $\textup{2, 4, and 16?}$

Explanation

To find the lowest common multiply, we need to find the smallest value which is a factor of each of the three numbers. We know it has to be even from the factor of two. If we look at the value , the lowest multiple of that number is Since the other two values are also divisible by this number, that is the lowest common multiple.

What is the least common multiple of $\textup{2, 4, and 16?}$

Explanation

If ab < 96 and b is a multiple of 4, what is the greatest possible value of a?

23.5

Explanation

Since we want a to be as large as possible, we want b to be as small as possible. The lowest possible value of b, then, is 4. If b is 4, then we can solve for a by setting up the equation:

4(a) = 96

96/4 = 24

If ab < 96 and b is a multiple of 4, what is the greatest possible value of a?

23.5

Explanation

Since we want a to be as large as possible, we want b to be as small as possible. The lowest possible value of b, then, is 4. If b is 4, then we can solve for a by setting up the equation:

4(a) = 96

96/4 = 24

What is the least common multiple of 4 and 6?