Find the LCM of the given numbers. See Example 3.
2, 3, 10
Example 3.
Find the LCM of 2, 3, and 10.
Strategy We will write the multiples of the largest number, 10, until we find one that is divisible by both of the smaller numbers, 2 and 3.
Why The LCM of 2, 3, and 10 is the smallest multiple of 10 that is divisible by 2 and 3.
Solution
The 1st multiple of 10: 10 · 1 = 10 ← 10 is divisible by 2, but not by 3. Find the next multiple.
The 2nd multiple of 10: 10 · 2 = 20 ← 20 is divisible by 2, but not by 3. Find the next multiple.
The 3rd multiple of 10: 10 · 3 = 30 ← 30 is divisible by 2 and by 3. It is the LCM.
The first multiple of 10 that is divisible by 2 and 3 is 30. Thus,
LCM (2, 3, 10) = 30 Read as “The least common multiple of 2, 3, and 10 is 30.”
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