Math Circles Prime Time Worksheet With Answers - Grade 6 - University Of Waterloo - 2015 Page 6
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10Lowest Common Multiple
A multiple of a number is the product of the number and another whole number.
Factors and multiples are closely related. For example, 9 is a factor of 90, so 90 is a multi-
ple of 9.
The least common multiple or LCM of two or more numbers is the smallest number that is
a multiple of each of the numbers.
We’re going to examine two different ways of finding the LCM:
Method 1
List the multiples of each number until you find the lowest one that is a common multiple
of all the numbers. This is the LCM.
Method 2
Begin by finding the prime factorization of each of the numbers. Then multiply each factor
the greatest number of times it occurs in any of the numbers. If the same factor occurs more
than once in all the numbers, you multiply the factor the greatest number of times it occurs.
Example: Find the LCM of 27 and 18.
Solution:
Using Method 1:
18: 18, 36, 54
27: 27, 54
the LCM is 54.
OR
Using Method 2:
18 =
2
3
3
27 =
3
3
3
the LCM is 2
3
3
3 = 54.
Try it out:
Find the LCM of the following groups of numbers.
1. 12 and 18
36
2. 36 and 64
576
3. 50 and 75 and 9
450
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