Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 35 and 10, is defined as the smallest positive integer that is divisible by both. It is written as LCM(35, 10).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 35 and 10 is 70, where 35 and 10 are less than 70.
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(35, 10) = LCM(10, 35).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 35 and 10 by Listing Method

Example: Find lcm of 35 and 10 by Listing Method

  • Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350
  • Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350

Hence, LCM of 35 and 10 is 70.

Steps to find LCM of 35 and 10 by Common Division Method

Example: Find lcm of 35 and 10 by Common Division Method

2 35 10
5 35 5
7 7 1
1 1

Hence, LCM of 35 and 10 is 2 x 5 x 7 = 70.

Steps to find lcm of 35 and 10 by Formula

Example: Find lcm of 35 and 10 by Formula

  • GCF of 35 and 10 = 5
  • LCM of 35 and 10 = (35 x 10) / 5
  • => 350 / 5

Hence, LCM of 35 and 10 is 70.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 35 and 10 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 35 and 10 minutes respectively to go round once. We need to find out at what time (minimum) they will run together again. For this we need to find the LCM of 35 and 10.
So, LCM of 35 and 10 is 70.

Both the cricket team and the rugby team had games, today. The cricket team plays every 35 days and the basketball team plays every 10 days. When will both teams have games on the same day again?

Given that the cricket team plays every 35 days and the basketball team plays every 10 days, so for finding the next time when both teams will play again we need to find the LCM of 35 and 10.
So, LCM of 35 and 10 is 70.

Steve spends 35 dollars every day while George spends 10 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 35 and 10.
So, LCM of 35 and 10 is 70.

Boxes that are 35 inches tall are being pilled next to boxes that are 10 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 35 and 10.
So, LCM of 35 and 10 is 70.

Find the LCM of 35 and 10 using GCF method.

Greatest common factor or gcf of 35 and 10 is GCF(35, 10) x LCM(35, 10) = (35 x 10) / GCF(35, 10) = 70.

Find the least common multiple of 35 and 10.

Least common multiple of 35 and 10 is 70.

Find the least number which is exactly divisible by 35 and 10.

Least number which is exactly divisible by 35 and 10 is 70.