Greatest Common Divisor

The greatest common divisor (GCD), which is also known as the greatest common factor (GCF), of two or more integers is the largest integer that is a common divisor (factor) of all the given integers.

The greatest common divisor of two or more integers can be obtained in three steps:

STEP 1: Find the prime factorization of each integer.

375 = 3 × 53
525 = 3 × 52 × 7

STEP 2: List the common prime divisors (factors) with the least power of all the given integers.

375 = 3 × 53 = 3 × 52 × 5
525 = 3 × 52 × 7 = 3 × 52 × 7

Common Prime Divisors (Factors) with Least Power: 3 and 52

STEP 3: Multiply the common prime divisors (factors) to find the greatest common divisor (factor).

3 × 52 = 75

GCD (GCF) of 375 and 525 = 75

Least Common Multiple

The least common multiple (LCM), which is also known as the least common denominator (LCD) in fractions, of two or more integers is the smallest integer that is a common multiple (denominator) of all the given integers.

The least common multiple (denominator) of two or more integers can be obtained in three steps:

STEP 1: Find the prime factorization of each integer.

  4 = 22
10 = 2 × 5
45 = 32 × 5

STEP 2: List the prime divisors (factors) with the greatest power of all the given integers.

  4 = 22
10 = 2 × 5
45 = 32 × 5

Prime Divisors (Factors) with Greatest Power: 22, 32, and 5

STEP 3: Multiply the prime divisors (factors) to find the least common multiple (denominator).

22 × 32 × 5 = 180

LCM of 4, 10 and 45 = 180