Least Common Multiple Sample Problems

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Here are some tips for Least Common Multiple, which aligns with New York state standards:

Least Common Multiple

Method One

The simplest way to find the least common multiple of two numbers is to list the multiples of each number and pick the first common occurrence.

Example 1: Find the LCM of 3 and 4
Multiples of 3: 3,6,9,12,15,18,21,24
Multiples of 4: 4,8,12,16,20,24
Both 12 and 24 are common multiples of 3 and 4, but 12 is smaller, so 12 is the least common multiple.

Method Two

Figure out the prime factorization of each number, multiply the common prime factors by the remaining factors

Example 2: Find the LCM of 8 and 12
Prime factors of 8: 2*2*2
Prime factors of 12: 2*2*3
LCM = 2*2*2*3 = 24

Method Three

Mutliply the numbers together and dividing by the GCF

Example 3: Find the LCM of 3 and 4
The GCF of 3 and 4 is 1.
The LCM is 3 * 4 / 1 = 12.

Example 4: Find the LCM of 6 and 15
The GCF of 6 and 15 is 3.
The LCM of 6 and 15 is 6 * 15 / 3 = 6 * 5 = 30