What is the Least Common Multiple of 546 and 550?
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 546 and 550 is 150150.
LCM(546,550) = 150150
Least Common Multiple of 546 and 550 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 546 and 550, than apply into the LCM equation.
GCF(546,550) = 2
LCM(546,550) = ( 546 × 550) / 2
LCM(546,550) = 300300 / 2
LCM(546,550) = 150150
Least Common Multiple (LCM) of 546 and 550 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 546 and 550. First we will calculate the prime factors of 546 and 550.
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
Prime Factorization of 550
Prime factors of 550 are 2, 5, 11. Prime factorization of 550 in exponential form is:
550 = 21 × 52 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 546 and 550.
LCM(546,550) = 21 × 31 × 71 × 131 × 52 × 111
LCM(546,550) = 150150
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