LCM for 15, 175 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 15, 175 and 225?

Answer

LCM of 15, 175 and 225 is
1,575

(One thousand five hundred seventy-five)

1,575 is the smallest positive integer that 15, 175 and 225 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 15, 175 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 15: 3 × 5 (exponent form: 3 × 5)

All Prime Factors of 175: 5 × 5 × 7 (exponent form: 52 × 7)

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

Prime factor15175225Highest power
33—3232
55525252
7—7—7

LCM = 32 × 52 × 7 = 1,575

Checking the LCM of 15, 175 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(15, 175) = (15 × 175) ÷ 5 = 2,625 ÷ 5 = 525

LCM(525, 225) = (525 × 225) ÷ 75 = 118,125 ÷ 75 = 1,575

LCM(15, 175, 225) = 1,575

The pairs may be taken in any order — 175 and 225 first, then 15 — and the answer is the same 1,575. 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 15, 175 and 225? (The answer is: 1,575). Enter the first number (e.g. '15'), the second (e.g. '175') 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
151752101,050
15175211110,775
15175212111,300
1517521337,275
15175214112,350
1517521522,575
1517521637,800
1517521716,275
15175218114,450
1517521938,325
1517522023,100
15175221116,025
1517522238,850
15175223117,075
1517522416,800
151752251,575
15175226118,650
15175227119,175
1517522839,900
15175229120,225
1517523024,150
151752315,775
15175232121,800
15175233122,325
1517523440,950
1517523524,675
15175236123,900
1517523741,475
1517523817,850
15175239125,475

FAQ

What's the Least Common Multiple (LCM) of 15, 175 and 225?

LCM of 15, 175 and 225 is 1,575

How to find the LCM of 15, 175 and 225 by prime factorization?

Take every prime that appears in 15, 175 and 225 to the highest power it reaches in any one of them and multiply: 3² × 5² × 7 = 1,575.

Can you get the LCM of 15, 175 and 225 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 15 and 175 is 525, and the LCM of 525 and 225 is 1,575 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,575 divisible by 15, 175 and 225?

Yes, and by definition it is the smallest positive integer that is: 1,575 ÷ 15, 1,575 ÷ 175 and 1,575 ÷ 225 all come out whole. Any other common multiple of 15, 175 and 225 is a multiple of 1,575.

See Also