Prime Factorization Method
There are multiple ways to find the least common multiple of given integers. In this method, we find the prime factors of each number, and then take the highest power of each prime that appears in the factorization of either number for find LCM.
- Find the prime factorization of each number:
35 = 5, 7
18 = 2, 3, 3
- Identify the highest powers of all prime numbers that appear in the factorization:
- To find LCM multiply these highest powers: LCM(35, 18) = = 630
Listing All Common Factors Method
To find the Least Common Multiple (LCM) of 35 and 18 using the method of listing common multiples, follow these steps:
- List some multiples of each number.
- Identify the smallest multiple that is common to both lists.
- Multiples of 35
35, 70, 105, 140, 175, 210, 245, 280, 315, 350,…
- Multiples of 18
18, 36, 54, 72, 90, 108, 126, 144, 162, 180,…
- Common multiples
Identify the common multiples from the lists above: 630, 1260,…
The smallest common multiple is 630.
The LCM of 35 and 18 using the common multiples method is 630.
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