What is the Least Common Multiple of 420 and 438?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 420 and 438 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 438, than apply into the LCM equation.

GCF(420,438) = 6
LCM(420,438) = ( 420 × 438) / 6
LCM(420,438) = 183960 / 6
LCM(420,438) = 30660

Least Common Multiple (LCM) of 420 and 438 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 438. First we will calculate the prime factors of 420 and 438.

Prime Factorization of 420

Prime Factorization of 438

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 438.

LCM(420,438) = 2² × 3¹ × 5¹ × 7¹ × 73¹
LCM(420,438) = 30660