What is the Least Common Multiple of 67122 and 67132?
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 67122 and 67132 is 2253017052.
LCM(67122,67132) = 2253017052
Least Common Multiple of 67122 and 67132 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67122 and 67132, than apply into the LCM equation.
GCF(67122,67132) = 2
LCM(67122,67132) = ( 67122 × 67132) / 2
LCM(67122,67132) = 4506034104 / 2
LCM(67122,67132) = 2253017052
Least Common Multiple (LCM) of 67122 and 67132 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 67122 and 67132. First we will calculate the prime factors of 67122 and 67132.
Prime Factorization of 67122
Prime factors of 67122 are 2, 3, 11, 113. Prime factorization of 67122 in exponential form is:
67122 = 21 × 33 × 111 × 1131
Prime Factorization of 67132
Prime factors of 67132 are 2, 13, 1291. Prime factorization of 67132 in exponential form is:
67132 = 22 × 131 × 12911
Now multiplying the highest exponent prime factors to calculate the LCM of 67122 and 67132.
LCM(67122,67132) = 22 × 33 × 111 × 1131 × 131 × 12911
LCM(67122,67132) = 2253017052
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