LCM for 120 and 180

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What's the Least Common Multiple (LCM) of 120 and 180?

Answer

LCM of 120 and 180 is
360

First common multiples: 360; 720; 1,080; …

360 is divisible by both: 360 ÷ 120 = 3, 360 ÷ 180 = 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/120 by 3 and of y/180 by 2.

120 = 23 × 3 × 5

180 = 22 × 32 × 5

Prime120180Highest power
2232223
333232
5555

LCM = 23 × 32 × 5 = 360

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LCM Table

Number 1Number 2LCM
1201651,320
1201669,960
12016720,040
120168840
12016920,280
1201702,040
1201716,840
1201725,160
12017320,760
1201743,480
1201754,200
1201762,640
1201777,080
12017810,680
12017921,480
120180360
12018121,720
12018210,920
1201837,320
1201842,760
1201854,440
1201863,720
12018722,440
1201885,640
1201897,560
1201902,280
12019122,920
120192960
12019323,160
12019411,640

FAQ

What's the Least Common Multiple (LCM) of 120 and 180?

LCM of 120 and 180 is 360

How to find the LCM of 120 and 180 using prime factorization?

To find the LCM of 120 and 180, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 360.

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 120 and 180: LCM = 360, GCF = 60.

See Also