What is the Least Common Multiple of 105 and 112?
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 105 and 112 is 1680.
LCM(105,112) = 1680
Least Common Multiple of 105 and 112 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 105 and 112, than apply into the LCM equation.
GCF(105,112) = 7
LCM(105,112) = ( 105 × 112) / 7
LCM(105,112) = 11760 / 7
LCM(105,112) = 1680
Least Common Multiple (LCM) of 105 and 112 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 105 and 112. First we will calculate the prime factors of 105 and 112.
Prime Factorization of 105
Prime factors of 105 are 3, 5, 7. Prime factorization of 105 in exponential form is:
105 = 31 × 51 × 71
Prime Factorization of 112
Prime factors of 112 are 2, 7. Prime factorization of 112 in exponential form is:
112 = 24 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 105 and 112.
LCM(105,112) = 31 × 51 × 71 × 24
LCM(105,112) = 1680
Related Least Common Multiples of 105
- LCM of 105 and 109
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- LCM of 105 and 111
- LCM of 105 and 112
- LCM of 105 and 113
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Related Least Common Multiples of 112
- LCM of 112 and 116
- LCM of 112 and 117
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- LCM of 112 and 119
- LCM of 112 and 120
- LCM of 112 and 121
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