What is the Least Common Multiple of 1398 and 1410?

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 1398 and 1410 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1398 and 1410, than apply into the LCM equation.

GCF(1398,1410) = 6
LCM(1398,1410) = ( 1398 × 1410) / 6
LCM(1398,1410) = 1971180 / 6
LCM(1398,1410) = 328530

Least Common Multiple (LCM) of 1398 and 1410 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1398 and 1410. First we will calculate the prime factors of 1398 and 1410.

Prime Factorization of 1398

Prime Factorization of 1410

Now multiplying the highest exponent prime factors to calculate the LCM of 1398 and 1410.

LCM(1398,1410) = 2¹ × 3¹ × 233¹ × 5¹ × 47¹
LCM(1398,1410) = 328530