# Least common multiple calculator

### LCM(6, 9) = 2×3^{2} = 18

##### 6 = 2×3

##### 9 = 3^{2}

##### LCM = 2×3^{2} = 18

#### 18 / 6 = 3

#### 18 / 9 = 2

### 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.

One way to find the least common multiple of two numbers is first to list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.

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

## Questions and word problems to LCM

- Three buses

Three public transport buses depart together from the bus station in the morning. The first bus was returning to the station after 18 minutes, the second after 12 minutes and a third after 24 minutes. How long will again together on the station? Result ex - Dressmaker

Dressmaker left a piece of canvas shorter than 5 meters. She is deciding whether it sew a skirt or dress. The canvas was exactly as much as they consumed had cut up her skirt to 120 cm, or 180 centimeters dress. What a piece of canvas left her? - LCM of two number

Find the smallest multiple of 63 and 147 - Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1. - 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 found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros - Buses

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

Gearing consists of two wheels, one is 88 and second 56 teeth. How many times turns smaller wheel to fit the same teeth as in the beginning? How many times will turn biggest wheel? - Buses 4

intervals: 1st bus 40 min. 2nd bus 2h 3rd bud 20min How long take them to meet - as soon as possible? - Four classses

Students of all 7, 8 and 9 classes in one school may take up 4,5,6 and 7 abreast and nobody will left. How many is the average count of pupils in one class if there are always four classes each grade? - 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 - A rope

A rope can be cut into equal length with no rope left over. The lengths can be 15cm,18cm or 25cm. What is the shortest possible length of the rope? - Dinosaurs

More than 30 and less than 60 dinosaurs have met at the pond. A quarter of them bathed and 1/7 saws, and the rest gripped. How many were at the pond? How many were there? - Athletes

Athletes at the stadium could enter two-steps, three-steps, four-steps, five-steps, six-steps. There were more than 100 but less than 200. How many athletes were there? - The tickets

The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices. - Ratio

Alena collected 7.8 kg of blueberries, 2.6 kg of blackberries, and 3.9 kg of cranberries. Express the ratio in the smallest natural numbers in this order. - Lamps on playground

The playground has the shape of a rectangle 36 x 50m. After how many meters will he place the lamps on his lighting, if the distances between them are to be the same on both sides if the builders want to use the smallest possible number of lamps?

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