LCM for 4, 9 and 16

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

What's the Least Common Multiple (LCM) of 4, 9 and 16?

Answer

LCM of 4, 9 and 16 is
144

(One hundred forty-four)

144 is the smallest positive integer that 4, 9 and 16 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 9 and 16 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

Prime factor4916Highest power
222—2424
3—32—32

LCM = 24 × 32 = 144

Checking the LCM of 4, 9 and 16 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, 16) = (36 × 16) ÷ 4 = 576 ÷ 4 = 144

LCM(4, 9, 16) = 144

The pairs may be taken in any order — 9 and 16 first, then 4 — and the answer is the same 144. 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 16? (The answer is: 144). Enter the first number (e.g. '4'), the second (e.g. '9') and the third (e.g. '16'), 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
14936
24936
34936
44936
459180
46936
479252
48972
49936
4910180
4911396
491236
4913468
4914252
4915180
4916144
4917612
491836
4919684
4920180
4921252
4922396
4923828
492472
4925900
4926468
4927108
4928252
49291,044
4930180

FAQ

What's the Least Common Multiple (LCM) of 4, 9 and 16?

LCM of 4, 9 and 16 is 144

How to find the LCM of 4, 9 and 16 by prime factorization?

Take every prime that appears in 4, 9 and 16 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

Can you get the LCM of 4, 9 and 16 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 16 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 144 divisible by 4, 9 and 16?

Yes, and by definition it is the smallest positive integer that is: 144 ÷ 4, 144 ÷ 9 and 144 ÷ 16 all come out whole. Any other common multiple of 4, 9 and 16 is a multiple of 144.

See Also