LCM Questions with Solution

Question 1: Find the LCM of 9, 12 and 15.

Answer:

Using Division Method,

LCM(9, 12 , 15) = 2 x 2 x 3 x 3 x 5 = 180

Question 2: Find the LCM of 8, 12 and 18.

Answer:

Using Prime Factorisation Method,

8 = 2 x 2 x 2

12 = 2 x 2 x3

18 = 2 x 3 x 3

Remember always consider prime factors that has the maximum count.

LCM(8, 12, 18) = 2 x 2 x 2 x 3 x 3 = 72

Question 3: Can the LCM of two numbers be smaller than both numbers?

Answer:

No, the LCM of two numbers cannot be smaller than both of those numbers. The LCM is defined as the smallest multiple that both numbers share in common.

Mathematically, if you have two numbers, let’s say ‘a’ and ‘b,’ where ‘a’ and ‘b’ are positive integers, then:

LCM(a, b) ≥ a and LCM(a, b) ≥ b

Hence LCM is always greater than or equal to both of the original numbers.

Question 4: Can the LCM of two numbers be zero?

Answer:

No, the LCM of two non-zero numbers cannot be zero. The LCM is defined as the smallest positive multiple that two numbers have in common. Since it’s the smallest multiple, it must be greater than or equal to 1.

Mathematically, if you have two non-zero numbers, ‘a’ and ‘b,’ where ‘a’ and ‘b’ are positive integers:

LCM(a, b) > 0

This means that the LCM is always a positive integer and cannot be zero, regardless of the values of ‘a’ and ‘b.’ Zero is not a valid LCM because it does not represent a common multiple of two non-zero numbers.

Question 5: Sarah is making friendship bracelets. She wants to make bracelets that are 8 inches long and 12 inches long. What is the smallest length of string she can use for each bracelet if she doesn’t want to have any leftover string?

Answer:

To find the smallest length of string that Sarah can use for each bracelet without any leftover string, we need to calculate the LCM of 8 inches and 12 inches.

Prime Factorisation Method ,

8 = 2 x 2 x 2

12 = 2 x 2 x 3

LCM(8, 12) = 2 x 2 x 2 x3 = 24

The smallest number that appears in both lists is 24. Hence Sarah needs a string that is 24 inches long for each bracelet to avoid any leftover string.

Question 6: Emily is a gardener, and she wants to plant flowers in her garden in rows. She has two types of flowers: roses and tulips. Emily wants to plant her flowers in rows such that each row contains the same number of each type of flower. She has 6 rose plants and 8 tulip plants. What is the maximum number of plants Emily can put in each row so that no plants are left over?

Answer:

To find the maximum number of plants Emily can put in each row so that no plants are left over, we need to calculate the LCM of the number of rose plants and the number of tulip plants.

Using Division Method,

LCM(6, 8) = 2 x 3 x 4 =24

The smallest number that appears in both lists is 24. Hence, Emily can plant 24 plants in each row, with 12 roses and 12 tulips, so that no plants are left over.

HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental concepts in mathematics, particularly in number theory. HCF is the highest common number which can exactly divide the two given numbers. LCM or Lowest Common Multiple is the common number that is divisible by both the given numbers. These concepts are essential tools for solving a wide range of mathematical problems.

In this article, we will learn about the definitions of HCF and LCM, their properties, and methods for calculating HCF and LCM. Along with this, all the possible varieties of HCF and LCM Questions have been discussed with solutions, and practice questions are provided on HCF and LCM for learners.