LCM for 4, 9 and 36

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

What's the Least Common Multiple (LCM) of 4, 9 and 36?

Answer

LCM of 4, 9 and 36 is
36

(Thirty-six)

36 is the smallest positive integer that 4, 9 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 9 and 36 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 4: 2 × 2 (exponent form: 22)

All Prime Factors of 9: 3 × 3 (exponent form: 32)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor4936Highest power
222—2222
3—323232

LCM = 22 × 32 = 36

Checking the LCM of 4, 9 and 36 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(4, 9) = (4 × 9) ÷ 1 = 36 ÷ 1 = 36

LCM(36, 36) = (36 × 36) ÷ 36 = 1,296 ÷ 36 = 36

LCM(4, 9, 36) = 36

The pairs may be taken in any order — 9 and 36 first, then 4 — and the answer is the same 36. That is exactly why the two routes on this page agree.

Related Calculations

See Also

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 4, 9 and 36? (The answer is: 36). Enter the first number (e.g. '4'), the second (e.g. '9') and the third (e.g. '36'), 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
4921252
4922396
4923828
492472
4925900
4926468
4927108
4928252
49291,044
4930180
49311,116
4932288
4933396
4934612
49351,260
493636
49371,332
4938684
4939468
4940360
49411,476
4942252
49431,548
4944396
4945180
4946828
49471,692
4948144
49491,764
4950900

FAQ

What's the Least Common Multiple (LCM) of 4, 9 and 36?

LCM of 4, 9 and 36 is 36

How to find the LCM of 4, 9 and 36 by prime factorization?

Take every prime that appears in 4, 9 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² = 36.

Can you get the LCM of 4, 9 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 9 is 36, and the LCM of 36 and 36 is 36 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 36 divisible by 4, 9 and 36?

Yes, and by definition it is the smallest positive integer that is: 36 ÷ 4, 36 ÷ 9 and 36 ÷ 36 all come out whole. Any other common multiple of 4, 9 and 36 is a multiple of 36.

See Also