What is the Least Common Multiple of 3504 and 3510?

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 3504 and 3510 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3504 and 3510, than apply into the LCM equation.

GCF(3504,3510) = 6
LCM(3504,3510) = ( 3504 × 3510) / 6
LCM(3504,3510) = 12299040 / 6
LCM(3504,3510) = 2049840

Least Common Multiple (LCM) of 3504 and 3510 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3504 and 3510. First we will calculate the prime factors of 3504 and 3510.

Prime Factorization of 3504

Prime Factorization of 3510

Now multiplying the highest exponent prime factors to calculate the LCM of 3504 and 3510.

LCM(3504,3510) = 2⁴ × 3³ × 73¹ × 5¹ × 13¹
LCM(3504,3510) = 2049840