LCM for 84 and 60

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What's the Least Common Multiple (LCM) of 84 and 60?

Answer

LCM of 84 and 60 is
420

First common multiples: 420; 840; 1,260; …

420 is divisible by both: 420 ÷ 84 = 5, 420 ÷ 60 = 7 — and 5 and 7 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/84 by 5 and of y/60 by 7.

84 = 22 × 3 × 7

60 = 22 × 3 × 5

Prime8460Highest power
2222222
3333
5—55
77—7

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 22 × 3 × 5 × 7 = 420

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LCM Table

Number 1Number 2LCM
84451,260
84461,932
84473,948
8448336
8449588
84502,100
84511,428
84521,092
84534,452
8454756
84554,620
8456168
84571,596
84582,436
84594,956
8460420
84615,124
84622,604
8463252
84641,344
84655,460
8466924
84675,628
84681,428
84691,932
8470420
84715,964
8472504
84736,132
84743,108

FAQ

What's the Least Common Multiple (LCM) of 84 and 60?

LCM of 84 and 60 is 420

How to find the LCM of 84 and 60 using prime factorization?

To find the LCM of 84 and 60, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 420.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 84 and 60: LCM = 420, GCF = 12.

See Also