What is the Least Common Multiple of 3420 and 3438?

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 3420 and 3438 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3420 and 3438, than apply into the LCM equation.

GCF(3420,3438) = 18
LCM(3420,3438) = ( 3420 × 3438) / 18
LCM(3420,3438) = 11757960 / 18
LCM(3420,3438) = 653220

Least Common Multiple (LCM) of 3420 and 3438 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3420 and 3438. First we will calculate the prime factors of 3420 and 3438.

Prime Factorization of 3420

Prime Factorization of 3438

Now multiplying the highest exponent prime factors to calculate the LCM of 3420 and 3438.

LCM(3420,3438) = 2² × 3² × 5¹ × 19¹ × 191¹
LCM(3420,3438) = 653220