Computers and Technology

# What is the Least Common Multiple (LCM)?

In mathematics, the least not unusual place more than one, additionally called the bottom not unusual place more than one of two (or more) integers a and b, is the smallest high-quality integer this is divisible through both. It is normally denoted as LCM (a, b).

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## Brute Force Method

There are more than one methods to discover a least not unusual place more than one. The maximum fundamental is without a doubt the usage of a “brute force” technique that lists out every integer’s multiples.

For example:-

Find LCM (18, 26) 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234 26: 52, 78, 104, 130, 156, 182, 208, 234 .

As are frequently seen, this technique may be pretty tedious, and is manner from ideal.

How to seek out lowest not unusual place more than one through Listing Multiples

• List the multiples of each range until at the least one in all of the multiples appears on all lists ·

Find the littlest wide variety it really is on all the lists ·  This wide variety is that the LCM Calculator

Example: LCM(6,7,21)

•  Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 ·
•  Multiples of 7: 7, 14, 21, 28, 35, 42, 56, 63 ·

Multiples of 21: 21, 42, 63 ·

Find the littlest range it really is on all the lists. we have got were given it in bold above. ·

So lowest not unusual place more than one(6, 7, a couple of1) is 42

How to seek out lowest not unusual place more than one through Prime Factorization

•      Find all of the top elements of each given wide variety. ·
•     List all of the top numbers located, as time and again as they arise maximum regularly for every person given wide variety. ·

Multiply the listing of top elements alongside to locate the LCM.

The LCM(a,b) is calculated through locating the top decision of every a and b. Use equal technique for the LCM of pretty 2 numbers.

For example, for LCM(12,30) we have a propensity to locate:

• Prime decision of twelve = 2 × 2 × three ·

Prime factorization of thirty = 2 × 3 × five ·

Using all top numbers located as frequently as each occurs maximum regularly we take 2 × 2 × 3 × 5 = 60 .         Therefore LCM(12,30) = 60.