What is the Least Common Multiple of 400 and 420?

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 400 and 420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 400 and 420, than apply into the LCM equation.

GCF(400,420) = 20
LCM(400,420) = ( 400 × 420) / 20
LCM(400,420) = 168000 / 20
LCM(400,420) = 8400

Least Common Multiple (LCM) of 400 and 420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 400 and 420. First we will calculate the prime factors of 400 and 420.

Prime Factorization of 400

Prime Factorization of 420

Now multiplying the highest exponent prime factors to calculate the LCM of 400 and 420.

LCM(400,420) = 2⁴ × 5² × 3¹ × 7¹
LCM(400,420) = 8400