Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 25 and 70, is defined as the smallest positive integer that is divisible by both. It is written as LCM(25, 70).

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(25, 70) = LCM(70, 25).
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is always greater than the given numbers numbers. Eg- LCM of 25 and 70 is 350, where 350 is greater than 25 and 70.

Steps to find lcm of 25 and 70 by Listing Method

Example: Find lcm of 25 and 70 by Listing Method

  • Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200, 1225, 1250, 1275, 1300, 1325, 1350, 1375, 1400, 1425, 1450, 1475, 1500, 1525, 1550, 1575, 1600, 1625, 1650, 1675, 1700, 1725, 1750
  • Multiples of 70: 70, 140, 210, 280, 350, 420, 490, 560, 630, 700, 770, 840, 910, 980, 1050, 1120, 1190, 1260, 1330, 1400, 1470, 1540, 1610, 1680, 1750

Hence, LCM of 25 and 70 is 350.

Steps to find LCM of 25 and 70 by Common Division Method

Example: Find lcm of 25 and 70 by Common Division Method

2 25 70
5 25 35
5 5 7
7 1 7
1 1

Hence, LCM of 25 and 70 is 2 x 5 x 5 x 7 = 350.

Steps to find lcm of 25 and 70 by Formula

Example: Find lcm of 25 and 70 by Formula

  • GCF of 25 and 70 = 5
  • LCM of 25 and 70 = (25 x 70) / 5
  • => 1750 / 5

Hence, LCM of 25 and 70 is 350.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 25 and 70 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 25 and 70 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 25 and 70.
So, LCM of 25 and 70 is 350.

A shopkeeper sells candies in packet of 25 and chocolates in packet of 70. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 25 and 70.
So, LCM of 25 and 70 is 350.

Boxes that are 25 inches tall are being pilled next to boxes that are 70 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 25 and 70.
So, LCM of 25 and 70 is 350.

Sammy's company prints 25 textbooks at a time. Daniel's company prints textbooks in sets of 70 at a time. According to a survey done by a committee, both companies printed the same number of textbooks last year. Find the least number of books that each company would have printed.

To find the least number of textbooks that each company could have printed we need to find the LCM of 25 and 70.
So, LCM of 25 and 70 is 350.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 25 and 70 is GCF(25, 70) * LCM(25, 70) = (25 x 70) / GCF(25, 70) = 350.

Find the least number which is exactly divisible by 25 and 70.

Least number which is exactly divisible by 25 and 70 is 350.

Find the LCM of 25 and 70 using GCF method.

Greatest common factor or gcf of 25 and 70 is GCF(25, 70) x LCM(25, 70) = (25 x 70) / GCF(25, 70) = 350.