Find HCF and LCM of 180 and 420 by Prime factorization method. Verify whether the HCF × LCM of these numbers is equal to the product of these numbers or not.
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Answer:
LCM = 3780
HCF = 20
Step-by-step explanation:
180 = 2×2×5×9
420 = 2×2×5×3×7
Writing all the numbers,
180 = 2² × 5¹ × 9¹ × 3° × 7°
420 = 2² × 5¹ × 9° × 3¹ × 7¹
LCM = 2² × 5¹ × 9¹ × 3¹ × 7¹ {Taking the numbers with higher degree}
LCM = 3780
HCF = 2² × 5¹ × 9° × 3° × 7° {Taking the numbers with lower degree}
HCF = 20
Now, HCF × LCM = 3780 × 20
= 75,600
And product of the two numbers
= 420 × 180
= 75,600
∴ HCF × LCM = Product of the two numbers.
Hence, verified.
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