LCM for 9 and 40

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What's the Least Common Multiple (LCM) of 9 and 40?

Answer

LCM of 9 and 40 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by both: 360 ÷ 9 = 40, 360 ÷ 40 = 9 — and 40 and 9 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/9 by 40 and of y/40 by 9.

9 and 40 are coprime (GCF = 1), so their LCM is simply the product: 9 × 40 = 360.

9 = 32

40 = 23 × 5

Prime940Highest power
2—2323
332—32
5—55

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

LCM = 23 × 32 × 5 = 360

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LCM Table

Number 1Number 2LCM
920180
92163
922198
92472
925225
92727
928252
929261
93090
932288
93399
935315
93636
938342
939117
940360
941369
943387
944396
94545
946414
948144
950450
951153
952468
95454
959531
96363
9100900
91211,089

FAQ

What's the Least Common Multiple (LCM) of 9 and 40?

LCM of 9 and 40 is 360

How to find the LCM of 9 and 40 using prime factorization?

To find the LCM of 9 and 40, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 360.

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 40: LCM = 360, GCF = 1.

See Also