LCM for 30 and 45

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What's the Least Common Multiple (LCM) of 30 and 45?

Answer

LCM of 30 and 45 is
90

First common multiples: 90, 180, 270, …

90 is divisible by both: 90 ÷ 30 = 3, 90 ÷ 45 = 2 — and 3 and 2 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/30 by 3 and of y/45 by 2.

30 = 2 × 3 × 5

45 = 32 × 5

Prime3045Highest power
22—2
333232
5555

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

LCM = 2 × 32 × 5 = 90

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LCM Table

Number 1Number 2LCM
3033330
3034510
3035210
3036180
30371,110
3038570
3040120
3042210
30431,290
304590
3046690
3050150
3055330
3056840
3057570
3058870
306060
3070210
3075150
3080240
3096480
30100300
30105210
30110330
30120120
30145870
30155930
30165330
30170510
30180180

FAQ

What's the Least Common Multiple (LCM) of 30 and 45?

LCM of 30 and 45 is 90

How to find the LCM of 30 and 45 using prime factorization?

To find the LCM of 30 and 45, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 90.

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 30 and 45: LCM = 90, GCF = 15.

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