If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 10 (Old)>Unit 1

Lesson 3: HCF and LCM

# HCF and LCM product

The product of the HCF and LCM of two numbers is equal to the product of the two numbers. Let's use this property to solve a few questions. We will prove why this is true in another video. Created by Aanand Srinivas. Created by Aanand Srinivas.

## Want to join the conversation?

• why product of lcm and hcf is equal to the product of the two numbers?i didnt got the logic behind this.
• HCF is the largest possible common factor, so it will divide both. LCM is the smallest possible multiple, so it can be divided by both of our numbers here. Let's say our numbers are 13 and 27 and we're asked to find out the LCM and HCF. If you use the traditional method to find out the HCF by prime factorisation, you'll find that the HCF is 1. Substituting our values in the equation, you'll get the following equation: 13*27=1x, where x is our unknown value. 13*27=351, which is equal to the right hand side of our equation as the RHS was multiplied by 1. This means x=351, which is the LCM for our two numbers. Take another example. Our two numbers are "xyzz" and "xyyz". The HCF would be "xyz" and the LCM would be "xyyzz". If you multiply both the numbers, you get: "xyzz"*"xyyz"="xxyyyzzz". If you multiply the LCM and HCF, you get: "xyz"*"xyyzz"="xxyyyzzz". Both the values are the same.
• Can we find the HCF of decimals?
• Is the HCF of a number is unique?
• Hi, can you also do this by dividing 6 from 18 and 12 and finding the two uncommon numbers and then multiply the uncommon numbers to 6 to get the LCM? How can we write this down with proper statements?
(1 vote)
• What do I do if I am following the steps but not getting the correct answer?
(1 vote)
• uh what if i get 2x6 2x3 2x5
(1 vote)
• At in the video,during the process,it's written that n2= 77/9 = 77. How was that obtained?
(1 vote)
• What if I have 2x2x7 2x3x7 and 2x5x7
(1 vote)
• The equation in the video won't work then, as that only works only for two numbers
(1 vote)