What is the Least Common Multiple of 49716 and 49728?
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 (LCM) of 49716 and 49728 is 206023104.
LCM(49716,49728) = 206023104
Least Common Multiple of 49716 and 49728 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49716 and 49728, than apply into the LCM equation.
GCF(49716,49728) = 12
LCM(49716,49728) = ( 49716 × 49728) / 12
LCM(49716,49728) = 2472277248 / 12
LCM(49716,49728) = 206023104
Least Common Multiple (LCM) of 49716 and 49728 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 49716 and 49728. First we will calculate the prime factors of 49716 and 49728.
Prime Factorization of 49716
Prime factors of 49716 are 2, 3, 1381. Prime factorization of 49716 in exponential form is:
49716 = 22 × 32 × 13811
Prime Factorization of 49728
Prime factors of 49728 are 2, 3, 7, 37. Prime factorization of 49728 in exponential form is:
49728 = 26 × 31 × 71 × 371
Now multiplying the highest exponent prime factors to calculate the LCM of 49716 and 49728.
LCM(49716,49728) = 26 × 32 × 13811 × 71 × 371
LCM(49716,49728) = 206023104
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