What is the Least Common Multiple of 30496 and 30500?
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 30496 and 30500 is 232532000.
LCM(30496,30500) = 232532000
Least Common Multiple of 30496 and 30500 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30496 and 30500, than apply into the LCM equation.
GCF(30496,30500) = 4
LCM(30496,30500) = ( 30496 × 30500) / 4
LCM(30496,30500) = 930128000 / 4
LCM(30496,30500) = 232532000
Least Common Multiple (LCM) of 30496 and 30500 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30496 and 30500. First we will calculate the prime factors of 30496 and 30500.
Prime Factorization of 30496
Prime factors of 30496 are 2, 953. Prime factorization of 30496 in exponential form is:
30496 = 25 × 9531
Prime Factorization of 30500
Prime factors of 30500 are 2, 5, 61. Prime factorization of 30500 in exponential form is:
30500 = 22 × 53 × 611
Now multiplying the highest exponent prime factors to calculate the LCM of 30496 and 30500.
LCM(30496,30500) = 25 × 9531 × 53 × 611
LCM(30496,30500) = 232532000
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