What is the Least Common Multiple of 3400 and 3420?

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 3400 and 3420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3400 and 3420, than apply into the LCM equation.

GCF(3400,3420) = 20
LCM(3400,3420) = ( 3400 × 3420) / 20
LCM(3400,3420) = 11628000 / 20
LCM(3400,3420) = 581400

Least Common Multiple (LCM) of 3400 and 3420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3400 and 3420. First we will calculate the prime factors of 3400 and 3420.

Prime Factorization of 3400

Prime Factorization of 3420

Now multiplying the highest exponent prime factors to calculate the LCM of 3400 and 3420.

LCM(3400,3420) = 2³ × 5² × 17¹ × 3² × 19¹
LCM(3400,3420) = 581400