LCM for 30, 36 and 48

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What's the Least Common Multiple (LCM) of 30, 36 and 48?

Answer

LCM of 30, 36 and 48 is
720

First common multiples: 720; 1,440; 2,160; …

720 is divisible by all three: 720 ÷ 30 = 24, 720 ÷ 36 = 20, 720 ÷ 48 = 15 — and 24, 20 and 15 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/30 by 24 and of y/36 by 20 and of z/48 by 15.

30 = 2 × 3 × 5

36 = 22 × 32

48 = 24 × 3

Prime303648Highest power
22222424
3332332
55——5

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

LCM = 24 × 32 × 5 = 720

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LCM Table

1st2nd3rdLCM
3033361,980
3034363,060
3035361,260
303636180
3036376,660
3036383,420
3036392,340
303640360
3036417,380
3036421,260
3036437,740
3036441,980
303645180
3036464,140
3036478,460
303648720
3036498,820
303650900
3036513,060
3036522,340
3036539,540
303654540
3036551,980
3036562,520
3036573,420
3036585,220
30365910,620
303660180
30366110,980
3036625,580

FAQ

What's the Least Common Multiple (LCM) of 30, 36 and 48?

LCM of 30, 36 and 48 is 720

How to find the LCM of 30, 36 and 48 by prime factorization?

Take every prime that appears in 30, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

Can you get the LCM of 30, 36 and 48 two numbers at a time?

Yes. The LCM of 30 and 36 is 180, and the LCM of 180 and 48 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 720 divisible by 30, 36 and 48?

Yes, and by definition it is the smallest positive integer that is: 720 ÷ 30, 720 ÷ 36 and 720 ÷ 48 all come out whole. Any other common multiple of 30, 36 and 48 is a multiple of 720.

See Also