What is the Least Common Multiple of 49296 and 49305?

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 49296 and 49305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49296 and 49305, than apply into the LCM equation.

GCF(49296,49305) = 3
LCM(49296,49305) = ( 49296 × 49305) / 3
LCM(49296,49305) = 2430539280 / 3
LCM(49296,49305) = 810179760

Least Common Multiple (LCM) of 49296 and 49305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49296 and 49305. First we will calculate the prime factors of 49296 and 49305.

Prime Factorization of 49296

Prime Factorization of 49305

Now multiplying the highest exponent prime factors to calculate the LCM of 49296 and 49305.

LCM(49296,49305) = 2⁴ × 3¹ × 13¹ × 79¹ × 5¹ × 19¹ × 173¹
LCM(49296,49305) = 810179760