LCM for 16, 28 and 40

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What's the Least Common Multiple (LCM) of 16, 28 and 40?

Answer

LCM of 16, 28 and 40 is
560

First common multiples: 560; 1,120; 1,680; …

560 is divisible by all three: 560 ÷ 16 = 35, 560 ÷ 28 = 20, 560 ÷ 40 = 14 — and 35, 20 and 14 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/16 by 35 and of y/28 by 20 and of z/40 by 14.

16 = 24

28 = 22 × 7

40 = 23 × 5

Prime162840Highest power
224222324
5——55
7—7—7

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

LCM = 24 × 5 × 7 = 560

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LCM Table

1st2nd3rdLCM
1625282,800
1626281,456
1627283,024
162828112
1628293,248
1628301,680
1628313,472
162832224
1628333,696
1628341,904
162835560
1628361,008
1628374,144
1628382,128
1628394,368
162840560
1628414,592
162842336
1628434,816
1628441,232
1628455,040
1628462,576
1628475,264
162848336
162849784
1628502,800
1628515,712
1628521,456
1628535,936
1628543,024

FAQ

What's the Least Common Multiple (LCM) of 16, 28 and 40?

LCM of 16, 28 and 40 is 560

How to find the LCM of 16, 28 and 40 by prime factorization?

Take every prime that appears in 16, 28 and 40 to the highest power it reaches in any one of them and multiply: 2⁴ × 5 × 7 = 560.

Can you get the LCM of 16, 28 and 40 two numbers at a time?

Yes. The LCM of 16 and 28 is 112, and the LCM of 112 and 40 is 560 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 560 divisible by 16, 28 and 40?

Yes, and by definition it is the smallest positive integer that is: 560 ÷ 16, 560 ÷ 28 and 560 ÷ 40 all come out whole. Any other common multiple of 16, 28 and 40 is a multiple of 560.

See Also