Find hcf and lcm of 520 and 468 by fundamental theorem of arithmetic (prime factorization) and verify the relationship. [HCFxLCM=product of 2 numbers]
Answers
Answer:
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Step-by-step explanation:
1. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the integers:
(i) 26 and 91
Solution:
Given integers are: 26 and 91
First, find the prime factors of 26 and 91.
26 = 2 × 13
91 = 7 × 13
∴ L.C.M (26, 91) = 2 × 7 × 13 = 182
And,
H.C.F (26, 91) = 13
Verification:
L.C.M × H.C.F = 182 x 13= 2366
And, product of the integers = 26 x 91 = 2366
∴ L.C.M × H.C.F = product of the integers
Hence verified.
(ii) 510 and 92
Solution:
Given integers are: 510 and 92
First, find the prime factors of 510 and 92.
510 = 2 × 3 × 5 × 17
92 = 2 × 2 × 23
∴ L.C.M (510, 92) = 2 × 2 × 3 × 5 × 23 × 17 = 23460
And,
H.C.F (510, 92) = 2
Verification:
L.C.M × H.C.F = 23460 x 2 = 46920
And, product of the integers = 510 x 92 = 46920
∴ L.C.M × H.C.F = product of the integers
Hence verified.
(iii) 336 and 54
Solution:
Given integers are: 336 and 54
First, find the prime factors of 336 and 54.
336 = 2 × 2 × 2 × 2 × 3 × 7
54 = 2 × 3 × 3 x 3
∴ L.C.M (336, 54) = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 = 3024
And,
H.C.F (336, 54) = 2 x 3 = 6
Verification:
L.C.M × H.C.F = 3024 x 6 = 18144
And, product of the integers = 336 x 54 = 18144
∴ L.C.M × H.C.F = product of the integers
Hence verified.