What is the Least Common Multiple of 1540 and 1547?

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 1540 and 1547 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1540 and 1547, than apply into the LCM equation.

GCF(1540,1547) = 7
LCM(1540,1547) = ( 1540 × 1547) / 7
LCM(1540,1547) = 2382380 / 7
LCM(1540,1547) = 340340

Least Common Multiple (LCM) of 1540 and 1547 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1540 and 1547. First we will calculate the prime factors of 1540 and 1547.

Prime Factorization of 1540

Prime Factorization of 1547

Now multiplying the highest exponent prime factors to calculate the LCM of 1540 and 1547.

LCM(1540,1547) = 2² × 5¹ × 7¹ × 11¹ × 13¹ × 17¹
LCM(1540,1547) = 340340