What is the LCM of 26 and 75?

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:

26 = 2, 13

75 = 3, 5, 5

• Identify the highest powers of all prime numbers that appear in the factorization: $2^1 × 3^1 × 5^2 × 13^1$
• To find LCM multiply these highest powers: LCM(26, 75) = $2^1 × 3^1 × 5^2 × 13^1$ = 1950

Listing All Common Factors Method

To find the Least Common Multiple (LCM) of 26 and 75 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 26

26, 52, 78, 104, 130, 156, 182, 208, 234, 260,…

• Multiples of 75

75, 150, 225, 300, 375, 450, 525, 600, 675, 750,…

• Common multiples

Identify the common multiples from the lists above: 1950, 3900,…

The smallest common multiple is 1950.

The LCM of 26 and 75 using the common multiples method is 1950.