What is the LCM of 835 and 18?

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:

835 = 5, 167

18 = 2, 3, 3

• Identify the highest powers of all prime numbers that appear in the factorization: $2^1 × 3^2 × 5^1 × 167^1$
• To find LCM multiply these highest powers: LCM(835, 18) = $2^1 × 3^2 × 5^1 × 167^1$ = 15030

Listing All Common Factors Method

To find the Least Common Multiple (LCM) of 835 and 18 using the method of listing common multiples, follow these steps:

1. List some multiples of each number.
2. Identify the smallest multiple that is common to both lists.

• Multiples of 835

835, 1670, 2505, 3340, 4175, 5010, 5845, 6680, 7515, 8350,…

• Multiples of 18

18, 36, 54, 72, 90, 108, 126, 144, 162, 180,…

• Common multiples

Identify the common multiples from the lists above: 15030, 30060,…

The smallest common multiple is 15030.

The LCM of 835 and 18 using the common multiples method is 15030.