Question

Find the LCM and HCF of 120 and 144 by fundamental theorem of arithmetic.

Answer 1

L.C.M. = 720 & H.C.F. = 24

To find:

Find the lowest common multiple (LCM) and highest common factor (HCF) of 120 and 144 by fundamental theorem of arithmetic.

Solution:

HCF is a largest number that “divides exactly into two or more numbers”.

LCM is two numbers is the “smallest number that they both divide evenly into”.

$120=2 \times 2 \times 2 \times 3 \times 5$

$144=2 \times 2 \times 2 \times 2 \times 3 \times 3$

$H C F=2 \times 2 \times 2 \times 3=24$

$L C M=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5=720$

Answer 2

Answer:

HCF(120,144)=24,

LCM(120,144)=720

Step-by-step explanation:

Fundamental Theorem of Arithmetic:

Every composite number can be expressed as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

We have ,

120 = 2³×3¹×5¹

144 = 2⁴×3²

HCF(120,144)=2³×3¹ = 8×3=24

/* Product of the smallest power of each common prime factors of the numbers */

LCM(120,144)=2⁴×3²×5¹

= 720

/* Product of the greatest power of each prime factors of the numbers */

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