LCM for 10, 17 and 26

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

What's the Least Common Multiple (LCM) of 10, 17 and 26?

Answer

LCM of 10, 17 and 26 is
2,210

(Two thousand two hundred ten)

2,210 is the smallest positive integer that 10, 17 and 26 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 17 and 26 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 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 17: 17 (exponent form: 17)

All Prime Factors of 26: 2 × 13 (exponent form: 2 × 13)

Prime factor101726Highest power
22—22
55——5
13——1313
17—17—17

LCM = 2 × 5 × 13 × 17 = 2,210

Checking the LCM of 10, 17 and 26 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(10, 17) = (10 × 17) ÷ 1 = 170 ÷ 1 = 170

LCM(170, 26) = (170 × 26) ÷ 2 = 4,420 ÷ 2 = 2,210

LCM(10, 17, 26) = 2,210

The pairs may be taken in any order — 17 and 26 first, then 10 — and the answer is the same 2,210. 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 10, 17 and 26? (The answer is: 2,210). Enter the first number (e.g. '10'), the second (e.g. '17') and the third (e.g. '26'), 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
1011171,870
1012171,020
1013172,210
1014171,190
101517510
1016171,360
101717170
1017181,530
1017193,230
101720340
1017213,570
1017221,870
1017233,910
1017242,040
101725850
1017262,210
1017274,590
1017282,380
1017294,930
101730510
1017315,270
1017322,720
1017335,610
101734170
1017351,190
1017363,060
1017376,290
1017383,230
1017396,630
101740680

FAQ

What's the Least Common Multiple (LCM) of 10, 17 and 26?

LCM of 10, 17 and 26 is 2,210

How to find the LCM of 10, 17 and 26 by prime factorization?

Take every prime that appears in 10, 17 and 26 to the highest power it reaches in any one of them and multiply: 2 × 5 × 13 × 17 = 2,210.

Can you get the LCM of 10, 17 and 26 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 17 is 170, and the LCM of 170 and 26 is 2,210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 2,210 divisible by 10, 17 and 26?

Yes, and by definition it is the smallest positive integer that is: 2,210 ÷ 10, 2,210 ÷ 17 and 2,210 ÷ 26 all come out whole. Any other common multiple of 10, 17 and 26 is a multiple of 2,210.

See Also