What is the Least Common Multiple of 414 and 429?

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 414 and 429 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 414 and 429, than apply into the LCM equation.

GCF(414,429) = 3
LCM(414,429) = ( 414 × 429) / 3
LCM(414,429) = 177606 / 3
LCM(414,429) = 59202

Least Common Multiple (LCM) of 414 and 429 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 429. First we will calculate the prime factors of 414 and 429.

Prime Factorization of 414

Prime Factorization of 429

Now multiplying the highest exponent prime factors to calculate the LCM of 414 and 429.

LCM(414,429) = 2¹ × 3² × 23¹ × 11¹ × 13¹
LCM(414,429) = 59202