LCM for 10, 100 and 1,000

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What's the Least Common Multiple (LCM) of 10, 100 and 1,000?

Answer

LCM of 10, 100 and 1,000 is
1,000

First common multiples: 1,000; 2,000; 3,000; …

1,000 is divisible by all three: 1,000 ÷ 10 = 100; 1,000 ÷ 100 = 10; 1,000 ÷ 1,000 = 1 — and 100, 10 and 1 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/10 by 100 and of y/100 by 10.

10 = 2 × 5

100 = 22 × 52

1,000 = 23 × 53

Prime101001,000Highest power
22222323
55525353

LCM = 23 × 53 = 1,000

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See Also

LCM Table

1st2nd3rdLCM
1010098519,700
1010098649,300
1010098798,700
1010098824,700
1010098998,900
101009909,900
1010099199,100
1010099224,800
1010099399,300
1010099449,700
1010099519,900
1010099624,900
1010099799,700
1010099849,900
1010099999,900
101001,0001,000
101001,001100,100
101001,00250,100
101001,003100,300
101001,00425,100
101001,00520,100
101001,00650,300
101001,007100,700
101001,00825,200
101001,009100,900
101001,01010,100
101001,011101,100
101001,01225,300
101001,013101,300
101001,01450,700

FAQ

What's the Least Common Multiple (LCM) of 10, 100 and 1,000?

LCM of 10, 100 and 1,000 is 1,000

How to find the LCM of 10, 100 and 1,000 by prime factorization?

Take every prime that appears in 10, 100 and 1,000 to the highest power it reaches in any one of them and multiply: 2³ × 5³ = 1,000.

Can you get the LCM of 10, 100 and 1,000 two numbers at a time?

Yes. The LCM of 10 and 100 is 100, and the LCM of 100 and 1,000 is 1,000 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,000 divisible by 10, 100 and 1,000?

Yes, and by definition it is the smallest positive integer that is: 1,000 ÷ 10, 1,000 ÷ 100 and 1,000 ÷ 1,000 all come out whole. Any other common multiple of 10, 100 and 1,000 is a multiple of 1,000.

See Also