Enhance your math knowledge by practicing the Word Problems Involving Least Common Multiple for free of cost. LCM will lay a stronger foundation in learning all other similar math concepts as well increases your problem-solving ability. Refer to the Word Problems on LCM available here and get an idea of how to solve LCM Questions using various methods. Be familiar with the concept and attempt the exams on different questions framed on Least Common Multiple with utmost confidence and score well.

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## LCM Word Problems with Answers

**Example 1.
**Find the lowest number which is exactly divisible by 12, 16

**Solution:**We have to find the Lcm to find the lowest number exactly divisible by 12,16.

**LCM= 2 ×2 × 3 × 4=48.**

Therefore, 48 is the lowest number exactly divisible by 12, 16.

**Example 2.
**Find the lowest number which is less by 3 to be divided by 18, 24,36

**Solution:**We find LCM of 18,24,36

**LCM=2 × 2 × 3 × 3 × 1 × 2 × 1 =72**

Now subtract 3 from 72 to get the required number.

72-3=69

Hence, 69 is the lowest number that divides 18,24,36.

**Example 3.
**A shopkeeper sells chocolate Packets that contain 15 chocolate and biscuit packets that contain 9 biscuits. What is the least number of chocolates and biscuits Siri should buy so that there will be one biscuit for every chocolate?

**Solution:**We have to find the LCM for Knowing how many chocolates and biscuits Siri should buy.

Multiples of 15 are 15,30,45,60,75

Multiples of 9 are 9,18,27,36,45,54

The lowest common multiple is 45.

The least number of chocolates and biscuits Siri should buy is 45.

**Example 4.
**A teacher has to arrange 25 students in different rows. Find out how many ways he can arrange the students with the same number in each row.

**Solution:**We have to find all the factors of 25.

25= 1× 25, 5 × 5

Factors of 25 are 1, 5, and 25.

A Teacher can arrange students in rows of 1, 5,25.

**Example 5.
**Pratima attends dance classes every 6 days, singing classes every 4 days, and yoga classes every 16 days. If she does all three activities today, in how many days will she do all the three activities again on the same day?

**Solution:**Multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48,52

Multiples of 6 are 6,12,18,24,30,36,42,48,54

Multiples of 16 are 16,32,48

In 48 days she will do all three on the same day.

**Example 6.
**Nevada goes shopping every 30 days. If she did shopping on Friday, find how many days she has to wait for shopping again on a Friday?

**Solution:**For finding a common multiple we have to multiply 30 days by 7 days in a week(to end up Friday again)

30 × 7=210.

Hence, Nevada has to wait for 210 days for shopping.

**Example 7.
**In an evening walk, three friends step off together. Their steps measure 55 cm, 70 cm, and 80 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

**Solution:**The distance covered by each of them is the same and minimum.

We have to find the LCM of the numbers 55,70 and 80.

The LCM of 55,70,80 is 2 × 5 × 11 ×7 ×8= 6160.

Hence, the minimum distance each should walk is 6160 cm.

**Example 8.**

Find the lowest number to be more by 5 that is exactly divisible by 40,60,80.

**Solution: **We find LCM of 40,60,80.

LCM of 40,60,80 is 2 ×2 ×2 ×5 ×1 ×3 × 2=240.

Therefore, the required number is 240+5=245.

**Example 9.
**A shopkeeper sells tea shirts 24 and pants 12. What is the least number of pants and shirts Pranavi should buy so that there will be one shirt for each pair of pant?

**Solution:**To find the least number of pants and shirts we find LCM.

Multiples of 24 are 24,48,72,96,120….

Multiples of 12 are 12,24,36,48,60……

The least common multiple is 24.

Hence, The least number of pants and shirts Pranavi should buy is 24.

**Example 10.
**Jagadish has to arrange 30 brinjal plants in different rows. Find out how many ways he can arrange the brinjal plants with the same number in each row.

**Solution:**We have to find all the factors of 30.

30= 1× 30, 2 ×15, 3 × 10, 5 × 6

Factors of 30 are 1,2,3,5,6,10, 15 and 30.

Jagadish can arrange brinjal plants in rows of 1,2,3,5,6,10,15,30.