How to find the least common multiple
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ACT Math › How to find the least common multiple
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?
24
30
56
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?
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
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 
If ab < 96 and b is a multiple of 4, what is the greatest possible value of a?
24
12
23.5
6
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?
10
12
16
20
24
Explanation
12 is the least common multiple of 4 and 6.
What is the least common multiple of 20, 16, and 32?
5
160
4
320
Explanation
The least comon multiple is the lowest multiple of all three numbers. 160 is 32x5, 16x10, and 8x20.
What is the least common multiple of 
There is no least common multiple becaues both numbers are prime.
Explanation
To find the least common multiple of two numbers, if they are both prime, simply multiply the numbers.
Thus we get that
We could also write out the multiples of each number and see what numbers they have in common. The least common multiple will be the common number that appears first in both sets.
