Solved Examples on LCM of 6 and 10

Some examples on LCM of 6 and 10

Example 1: You’re planning a party and want to serve both cupcakes (6 per batch) and cookies (10 per batch) to your guests. To ensure everyone gets an equal share, you need to find the smallest number of batches for each treat that results in the same number of cupcakes and cookies.

Solution:

LCM of 6 and 10 is 30

Therefore, you need to bake at least 5 batches of cupcakes (6 × 5 = 30) and 3 batches of cookies (10 × 3 = 30) to have 30 cupcakes and 30 cookies, enough for everyone to enjoy!

Example 2: Two friends, Maya and Alex, have different workout routines. Maya trains after every 6th day, while Alex does yoga after every 10th day. They starts at 1 of Jan and want to find the next time their workout schedules will coincide.

Solution:

LCM of 6 and 10 is 30

So, Maya and Alex will both be working out on the same day again every 30 days, the “common beat” of their schedules.

Example 3: Find the LCM of 10 and 6 using the listing multiples method.

Solution:

Multiples of 10: 10, 20, 30, 40, 50…

Multiples of 6: 6, 12, 18, 24, 30, 36…

Common multiple: 30

LCM(10, 6) = 30

Example 4: Explore the factors of 10 and 6 by choosing a larger set of prime factors and then using prime factorization calculate its LCM.

Solution:

10 = 2×5

6 = 2×3

Common Factor: 2

Uncommon Factors: 5 and 3

LCM(10,6) = 2×5×3 =30

LCM of 6 and 10 is 30. LCM or Least Common Multiple is the smallest multiple of both numbers. The concept of LCM is very important and is used in various problems of mathematics. In this article, we will discuss the concept of LCM and specifically explore its calculation for the numbers 10 and 6.