What is the Least Common Multiple of 34740 and 34749?

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 34740 and 34749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34740 and 34749, than apply into the LCM equation.

GCF(34740,34749) = 9
LCM(34740,34749) = ( 34740 × 34749) / 9
LCM(34740,34749) = 1207180260 / 9
LCM(34740,34749) = 134131140

Least Common Multiple (LCM) of 34740 and 34749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34740 and 34749. First we will calculate the prime factors of 34740 and 34749.

Prime Factorization of 34740

Prime Factorization of 34749

Now multiplying the highest exponent prime factors to calculate the LCM of 34740 and 34749.

LCM(34740,34749) = 2² × 3⁵ × 5¹ × 193¹ × 11¹ × 13¹
LCM(34740,34749) = 134131140