LCM for 3, 8 and 9

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

What's the Least Common Multiple (LCM) of 3, 8 and 9?

Answer

LCM of 3, 8 and 9 is
72

First common multiples: 72, 144, 216, …

72 is divisible by all three: 72 ÷ 3 = 24, 72 ÷ 8 = 9, 72 ÷ 9 = 8 — and 24, 9 and 8 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/3 by 24 and of y/8 by 9 and of z/9 by 8.

3 — prime

8 = 23

9 = 32

Prime389Highest power
2—23—23
33—3232

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

LCM = 23 × 32 = 72

More with these numbers

Related Calculations

See Also

LCM Table

1st2nd3rdLCM
13824
23824
33824
34824
358120
36824
378168
38824
38972
3810120
3811264
381224
3813312
3814168
3815120
381648
3817408
381872
3819456
3820120
3821168
3822264
3823552
382424
3825600
3826312
3827216
3828168
3829696
3830120

FAQ

What's the Least Common Multiple (LCM) of 3, 8 and 9?

LCM of 3, 8 and 9 is 72

How to find the LCM of 3, 8 and 9 by prime factorization?

Take every prime that appears in 3, 8 and 9 to the highest power it reaches in any one of them and multiply: 2³ × 3² = 72.

Can you get the LCM of 3, 8 and 9 two numbers at a time?

Yes. The LCM of 3 and 8 is 24, and the LCM of 24 and 9 is 72 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 72 divisible by 3, 8 and 9?

Yes, and by definition it is the smallest positive integer that is: 72 ÷ 3, 72 ÷ 8 and 72 ÷ 9 all come out whole. Any other common multiple of 3, 8 and 9 is a multiple of 72.

See Also