What is the Least Common Multiple of 35742 and 35760?

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 35742 and 35760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35742 and 35760, than apply into the LCM equation.

GCF(35742,35760) = 6
LCM(35742,35760) = ( 35742 × 35760) / 6
LCM(35742,35760) = 1278133920 / 6
LCM(35742,35760) = 213022320

Least Common Multiple (LCM) of 35742 and 35760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 35742 and 35760. First we will calculate the prime factors of 35742 and 35760.

Prime Factorization of 35742

Prime Factorization of 35760

Now multiplying the highest exponent prime factors to calculate the LCM of 35742 and 35760.

LCM(35742,35760) = 2⁴ × 3¹ × 7¹ × 23¹ × 37¹ × 5¹ × 149¹
LCM(35742,35760) = 213022320