LCM for 12 and 31

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What's the Least Common Multiple (LCM) of 12 and 31?

Answer

LCM of 12 and 31 is
372

First common multiples: 372; 744; 1,116; …

372 is divisible by both: 372 ÷ 12 = 31, 372 ÷ 31 = 12 — and 31 and 12 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/12 by 31 and of y/31 by 12.

12 and 31 are coprime (GCF = 1), so their LCM is simply the product: 12 × 31 = 372.

12 = 22 × 3

31 — prime

Prime1231Highest power
222—22
33—3
31—3131

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

LCM = 22 × 3 × 31 = 372

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LCM Table

Number 1Number 2LCM
121648
1217204
121836
1219228
122060
122184
1222132
1223276
122424
1225300
1226156
1227108
122884
1229348
123060
1231372
123296
1233132
1235420
123636
1239156
1240120
124284
1244132
1245180
1246276
124848
1250300
1252156
1254108

FAQ

What's the Least Common Multiple (LCM) of 12 and 31?

LCM of 12 and 31 is 372

How to find the LCM of 12 and 31 using prime factorization?

To find the LCM of 12 and 31, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 372.

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 12 and 31: LCM = 372, GCF = 1.

See Also