LCM for 45, 120 and 525

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

What's the Least Common Multiple (LCM) of 45, 120 and 525?

Answer

LCM of 45, 120 and 525 is
12,600

First common multiples: 12,600; 25,200; 37,800; …

12,600 is divisible by all three: 12,600 ÷ 45 = 280; 12,600 ÷ 120 = 105; 12,600 ÷ 525 = 24 — and 280, 105 and 24 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/45 by 280 and of y/120 by 105 and of z/525 by 24.

45 = 32 × 5

120 = 23 × 3 × 5

525 = 3 × 52 × 7

Prime45120525Highest power
2—23—23
3323332
5555252
7——77

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 23 × 32 × 52 × 7 = 12,600

More with these numbers

Related Calculations

See Also

LCM Table

1st2nd3rdLCM
451205106,120
45120511183,960
4512051223,040
4512051320,520
4512051492,520
4512051537,080
4512051615,480
45120517186,120
4512051893,240
4512051962,280
451205204,680
45120521187,560
4512052210,440
45120523188,280
4512052447,160
4512052512,600
4512052694,680
45120527189,720
451205287,920
45120529190,440
4512053019,080
4512053121,240
4512053247,880
45120533191,880
4512053432,040
4512053538,520
4512053624,120
4512053764,440
4512053896,840
45120539194,040

FAQ

What's the Least Common Multiple (LCM) of 45, 120 and 525?

LCM of 45, 120 and 525 is 12,600

How to find the LCM of 45, 120 and 525 by prime factorization?

Take every prime that appears in 45, 120 and 525 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5² × 7 = 12,600.

Can you get the LCM of 45, 120 and 525 two numbers at a time?

Yes. The LCM of 45 and 120 is 360, and the LCM of 360 and 525 is 12,600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 12,600 divisible by 45, 120 and 525?

Yes, and by definition it is the smallest positive integer that is: 12,600 ÷ 45, 12,600 ÷ 120 and 12,600 ÷ 525 all come out whole. Any other common multiple of 45, 120 and 525 is a multiple of 12,600.

See Also