LCM for 9, 75 and 105

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 9, 75 and 105?

Answer

LCM of 9, 75 and 105 is
1,575

(One thousand five hundred seventy-five)

1,575 is the smallest positive integer that 9, 75 and 105 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 9, 75 and 105 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 9: 3 × 3 (exponent form: 32)

All Prime Factors of 75: 3 × 5 × 5 (exponent form: 3 × 52)

All Prime Factors of 105: 3 × 5 × 7 (exponent form: 3 × 5 × 7)

Prime factor975105Highest power
3323332
5—52552
7——77

LCM = 32 × 52 × 7 = 1,575

Checking the LCM of 9, 75 and 105 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(9, 75) = (9 × 75) ÷ 3 = 675 ÷ 3 = 225

LCM(225, 105) = (225 × 105) ÷ 15 = 23,625 ÷ 15 = 1,575

LCM(9, 75, 105) = 1,575

The pairs may be taken in any order — 75 and 105 first, then 9 — and the answer is the same 1,575. 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 9, 75 and 105? (The answer is: 1,575). Enter the first number (e.g. '9'), the second (e.g. '75') and the third (e.g. '105'), 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
97590450
9759120,475
9759220,700
975936,975
9759421,150
975954,275
975967,200
9759721,825
9759822,050
975992,475
975100900
97510122,725
9751027,650
97510323,175
97510423,400
9751051,575
97510623,850
97510724,075
9751082,700
97510924,525
9751104,950
9751118,325
97511225,200
97511325,425
9751148,550
9751155,175
97511626,100
9751172,925
97511826,550
97511926,775

FAQ

What's the Least Common Multiple (LCM) of 9, 75 and 105?

LCM of 9, 75 and 105 is 1,575

How to find the LCM of 9, 75 and 105 by prime factorization?

Take every prime that appears in 9, 75 and 105 to the highest power it reaches in any one of them and multiply: 3² × 5² × 7 = 1,575.

Can you get the LCM of 9, 75 and 105 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 9 and 75 is 225, and the LCM of 225 and 105 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 9, 75 and 105?

Yes, and by definition it is the smallest positive integer that is: 1,575 ÷ 9, 1,575 ÷ 75 and 1,575 ÷ 105 all come out whole. Any other common multiple of 9, 75 and 105 is a multiple of 1,575.

See Also