LCM for 45 and 100

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What's the Least Common Multiple (LCM) of 45 and 100?

Answer

LCM of 45 and 100 is
900

First common multiples: 900; 1,800; 2,700; …

900 is divisible by both: 900 ÷ 45 = 20, 900 ÷ 100 = 9 — and 20 and 9 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/45 by 20 and of y/100 by 9.

45 = 32 × 5

100 = 22 × 52

Prime45100Highest power
2—2222
332—32
555252

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

LCM = 22 × 32 × 52 = 900

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LCM Table

Number 1Number 2LCM
45492,205
4550450
45522,340
45532,385
4554270
4555495
4557855
4560180
4563315
4565585
4570630
4572360
4575225
45763,420
4580720
4581405
45841,260
459090
4595855
4599495
45100900
45105315
45108540
45117585
45120360
451251,125
45135135
45150450
45180180
45405405

FAQ

What's the Least Common Multiple (LCM) of 45 and 100?

LCM of 45 and 100 is 900

How to find the LCM of 45 and 100 using prime factorization?

To find the LCM of 45 and 100, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 900.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 45 and 100: LCM = 900, GCF = 5.

See Also