LCM for 9 and 12

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What's the Least Common Multiple (LCM) of 9 and 12?

Answer

LCM of 9 and 12 is
36

First common multiples: 36, 72, 108, …

36 is divisible by both: 36 ÷ 9 = 4, 36 ÷ 12 = 3 — and 4 and 3 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/9 by 4 and of y/12 by 3.

9 = 32

12 = 22 × 3

Prime912Highest power
2—2222
332332

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

LCM = 22 × 32 = 36

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LCM Table

Number 1Number 2LCM
939
9436
9545
9618
9763
9872
91090
91199
91236
913117
914126
91545
916144
917153
91818
920180
92163
922198
92472
925225
92727
928252
929261
93090
932288
93399
935315
93636
938342
939117

FAQ

What's the Least Common Multiple (LCM) of 9 and 12?

LCM of 9 and 12 is 36

How to find the LCM of 9 and 12 using prime factorization?

To find the LCM of 9 and 12, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 36.

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 9 and 12: LCM = 36, GCF = 3.

See Also