**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 × 5^{3}
525 = 3 × 5^{2} ×
7
**STEP 2: List the common prime divisors (factors) with the least
power of all the given integers.**
375 = 3 × 5^{3}
= 3 × 5^{2}
× 5
525 = 3 × 5^{2}
× 7 = 3 × 5^{2}
× 7
Common Prime Divisors (Factors) with Least Power: 3
and 5^{2}
**STEP 3: Multiply the common prime divisors (factors) to find the
greatest common divisor (factor).**
3 × 5^{2}
= 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 = 2^{2}
10 = 2 × 5
45 = 3^{2} × 5
**STEP 2: List the prime divisors (factors) with the greatest
power of all the given integers.**
4 = 2^{2}
10 = 2 × 5
45 = 3^{2} × 5
Prime Divisors (Factors) with Greatest Power: 2^{2},
3^{2},
and 5
**STEP 3: Multiply the prime divisors (factors) to find the least common
multiple (denominator).**
2^{2} × 3^{2}
× 5 = 180
LCM of 4, 10 and 45 = 180 |