LCM for 10, 100 and 1,000

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

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

Answer

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

(One thousand)

1,000 is the smallest positive integer that 10, 100 and 1,000 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 100 and 1,000 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

All Prime Factors of 1,000: 2 × 2 × 2 × 5 × 5 × 5 (exponent form: 23 × 53)

Prime factor101001,000Highest power
22222323
55525353

LCM = 23 × 53 = 1,000

Checking the LCM of 10, 100 and 1,000 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(10, 100) = (10 × 100) ÷ 10 = 1,000 ÷ 10 = 100

LCM(100, 1,000) = (100 × 1,000) ÷ 100 = 100,000 ÷ 100 = 1,000

LCM(10, 100, 1,000) = 1,000

The pairs may be taken in any order — 100 and 1,000 first, then 10 — and the answer is the same 1,000. That is exactly why the two routes on this page agree.

Related Calculations

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About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 10, 100 and 1,000? (The answer is: 1,000). Enter the first number (e.g. '10'), the second (e.g. '100') and the third (e.g. '1,000'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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