LCM for 50, 150 and 225

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 50, 150 and 225?

Answer

LCM of 50, 150 and 225 is
450

(Four hundred fifty)

450 is the smallest positive integer that 50, 150 and 225 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 50, 150 and 225 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 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 150: 2 × 3 × 5 × 5 (exponent form: 2 × 3 × 52)

All Prime Factors of 225: 3 × 3 × 5 × 5 (exponent form: 32 × 52)

Prime factor50150225Highest power
222—2
3—33232
552525252

LCM = 2 × 32 × 52 = 450

Checking the LCM of 50, 150 and 225 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(50, 150) = (50 × 150) ÷ 50 = 7,500 ÷ 50 = 150

LCM(150, 225) = (150 × 225) ÷ 75 = 33,750 ÷ 75 = 450

LCM(50, 150, 225) = 450

The pairs may be taken in any order — 150 and 225 first, then 50 — and the answer is the same 450. That is exactly why the two routes on this page agree.

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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 50, 150 and 225? (The answer is: 450). Enter the first number (e.g. '50'), the second (e.g. '150') and the third (e.g. '225'), 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
501502101,050
5015021131,650
5015021215,900
5015021310,650
5015021416,050
501502156,450
501502165,400
5015021732,550
5015021816,350
5015021910,950
501502203,300
5015022133,150
501502225,550
5015022333,450
5015022416,800
50150225450
5015022616,950
5015022734,050
501502285,700
5015022934,350
501502303,450
5015023111,550
5015023217,400
5015023334,950
501502345,850
501502357,050
5015023617,700
5015023711,850
5015023817,850
5015023935,850

FAQ

What's the Least Common Multiple (LCM) of 50, 150 and 225?

LCM of 50, 150 and 225 is 450

How to find the LCM of 50, 150 and 225 by prime factorization?

Take every prime that appears in 50, 150 and 225 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5² = 450.

Can you get the LCM of 50, 150 and 225 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 50 and 150 is 150, and the LCM of 150 and 225 is 450 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 450 divisible by 50, 150 and 225?

Yes, and by definition it is the smallest positive integer that is: 450 ÷ 50, 450 ÷ 150 and 450 ÷ 225 all come out whole. Any other common multiple of 50, 150 and 225 is a multiple of 450.

See Also