Question

lcm and hcf of 84 90 120

Answer 1

“2520 and 6 are the LCM and HCF” of the given numbers 84, 90, 120 respectively.

To find:

The LCM and HCF of 84, 90, and 120.

Solution:

LCM means “Least Common Multiple”.

HCF means “Highest Common Factor”.

Factors of 84 = $2 \times 2 \times 3 \times 7$

Factors of 90 = $2 \times 3 \times 3 \times 5$

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

With the help of the factors, the LCM and HCF can be determined,

Hence LCM of 84 90 120 =$2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7$

$= 8 \times 9 \times 35$

=2520

Then, HCF of 84 90 120 = $2 \times 3$ =6

Answer 2

Answer:

HCF(84,90,120)=6

HCF(84,90,120)=6LCM(84,90,120)=2520

Step-by-step explanation:

We have ,

84 = 2×2×3×7 = 2²×3¹×7¹

90 = 2×3×3×5 = 2¹×3²×5¹

120 = 2×2×2×3×5=2³×3¹×5¹

HCF(84,90,120)=2¹×3¹=6

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

LCM(84,90,120)=2³×3²×5¹×7¹

=2520

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

Therefore,

HCF(84,90,120)=6

LCM(84,90,120)=2520

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