LCM for 31 and 34

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What's the Least Common Multiple (LCM) of 31 and 34?

Answer

LCM of 31 and 34 is
1,054

First common multiples: 1,054; 2,108; 3,162; …

1,054 is divisible by both: 1,054 ÷ 31 = 34; 1,054 ÷ 34 = 31 — and 34 and 31 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/31 by 34 and of y/34 by 31.

31 and 34 are coprime (GCF = 1), so their LCM is simply the product: 31 × 34 = 1,054.

31 — prime

34 = 2 × 17

Prime3134Highest power
2—22
17—1717
3131—31

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

LCM = 2 × 17 × 31 = 1,054

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LCM Table

Number 1Number 2LCM
3119589
3120620
3121651
3122682
3123713
3124744
3125775
3126806
3127837
3128868
3129899
3130930
313131
3132992
31331,023
31341,054
31351,085
31361,116
31371,147
31381,178
31391,209
31401,240
31411,271
31421,302
31431,333
31441,364
31451,395
31461,426
31471,457
31481,488

FAQ

What's the Least Common Multiple (LCM) of 31 and 34?

LCM of 31 and 34 is 1,054

How to find the LCM of 31 and 34 using prime factorization?

To find the LCM of 31 and 34, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 1,054.

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 31 and 34: LCM = 1,054, GCF = 1.

See Also