# Least common multiple calculator

### LCM(8, 5) = 2^{3}×5 = 40

##### 8 = 2^{3}

##### 5 = 5

##### LCM = 2^{3}×5 = 40

#### 40 / 8 = 5

#### 40 / 5 = 8

### What is LCM?

The least common multiple (also called the lowest common multiple or smallest common multiple or LCM) of one or more integer numbers is the smallest positive integer divisible by all these numbers.

So, how do you find the LCM of two numbers? It's simpler than you might think. First, list the prime factors of each number. Then, identify the factors that appear in both lists. Finally, multiply these common factors by the highest power they appear in either list. This will give you the LCM of the two numbers.

For three or more numbers, proceed similarly and multiply the largest found powers of prime factors of given numbers.

## Questions and word problems to LCM

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- Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1. - The grocery

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There are 159 students to be grouped into relay teams. Each team should have the same number of students. Can each team have 3,5 or 6 students? Explain. - LCM and HCF 2

If the product of two numbers is 5780 and their HCF is 17, then what is their LCM? - Around the flowerbed

Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses are found in every corner of the flowerbed and consumed as little as possible. a) At what distance are planted roses? b) How many rose

- Buses

At the bus stop at 10 o'clock met buses No. 2 and No. 9. Bus number 2 runs at an interval of 4 minutes and bus number 9 at intervals of 9 minutes. How many times does the bus meet at 18:00 local time? - Gearing

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Students of all 7, 8, and 9 classes in one school may take up 4, 5, 6, and 7 abreast, and nobody will be left. If there are always four classes in each grade, what is the average number of pupils in one class? - Gcd and lcm

Calculate the greatest common divisor and the least common multiple of numbers. a) 16 and 18 b) 24 and 22 c) 45 and 60 d) 36 and 30

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