What is the Least Common Multiple of 413 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 413 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 413 and 420, than apply into the LCM equation.

GCF(413,420) = 7
LCM(413,420) = ( 413 × 420) / 7
LCM(413,420) = 173460 / 7
LCM(413,420) = 24780

Least Common Multiple (LCM) of 413 and 420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 413 and 420. First we will calculate the prime factors of 413 and 420.

Prime Factorization of 413

Prime Factorization of 420

Now multiplying the highest exponent prime factors to calculate the LCM of 413 and 420.

LCM(413,420) = 7¹ × 59¹ × 2² × 3¹ × 5¹
LCM(413,420) = 24780