Find the LCM and HCF of 840 and 144 by applying the Fundamental Theore

1.	Find the LCM and HCF of 840 and 144 by applying the Fundamental Theorem of Arithmetic.
Answer» Fundamental theorem of arithmetic implies that we write a number in form of the products of its prime factors. We use this to get the LCM of two numbers by getting the prime numbers with the largest powers between the two numbers and getting their product. We get the HCF/GCD by getting only the prime factors that are present in both with taking the one with the least power between the two. 144=2^4 × 3^2 840=2^3 × 3^1 × 5^1 ×7^1 LCM=2^4 ×3^2 × 5 × 7=5040 HCF=2^3 × 3^1=24

Find the LCM and HCF of 840 and 144 by applying the Fundamental Theorem of Arithmetic.

Answer»

Fundamental theorem of arithmetic implies that we write a number in form of the products of its prime factors.

We use this to get the LCM of two numbers by getting the prime numbers with the largest powers between the two numbers and getting their product.

We get the HCF/GCD by getting only the prime factors that are present in both with taking the one with the least power between the two.

144=2^4 × 3^2

840=2^3 × 3^1 × 5^1 ×7^1

LCM=2^4 ×3^2 × 5 × 7=5040

HCF=2^3 × 3^1=24