What is the Least Common Multiple of 531 and 546?
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 531 and 546 is 96642.
LCM(531,546) = 96642
Least Common Multiple of 531 and 546 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 531 and 546, than apply into the LCM equation.
GCF(531,546) = 3
LCM(531,546) = ( 531 × 546) / 3
LCM(531,546) = 289926 / 3
LCM(531,546) = 96642
Least Common Multiple (LCM) of 531 and 546 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 531 and 546. First we will calculate the prime factors of 531 and 546.
Prime Factorization of 531
Prime factors of 531 are 3, 59. Prime factorization of 531 in exponential form is:
531 = 32 × 591
Prime Factorization of 546
Prime factors of 546 are 2, 3, 7, 13. Prime factorization of 546 in exponential form is:
546 = 21 × 31 × 71 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 531 and 546.
LCM(531,546) = 32 × 591 × 21 × 71 × 131
LCM(531,546) = 96642
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