2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
Answers
Answer:
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Step-by-step explanation:
(i) 26 and 91
Factor of 26=2×13×1
Factor of 91=7×13×1
HCF of 26 and 91=13×1=13
LCM of 26 and 91=2×7×13=182
LCM × HCF =182×13=2366
26×91=2366
So, LCM.HCF = product of the two numbers =26×91.
Hence proved.
(ii) 510×92
Factor of 510=2×3×5×17×1
Factor of 92=2×2×23
HCF of 510 and 92=2×2=2
LCM of 510 and 92=2×2×3×5×17×23=23,460
LCM × HCF =23,460×2=46,920
510×92=46,920
So, LCM.HCF = product of the two numbers =510×92.
Hence proved.
(iii) 336 and 54
Factor of 336=2×2×2×2×7×3×1
Factor of 54=2×3×3×3
HCF of 336 and 54=2×3=6
LCM of 336 and 54=2×3×2×2×2×7×3×3=3,024
LCM × HCF =3,024×6=18,144
366×54=18,144
So, LCM.HCF = product of the two numbers =336×54.
Hence proved.
Step-by-step explanation:
2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
(i) 26 and 91
(ii) 510 and 92
(iii) 336 and 54
Solutions:
(i) 26 and 91
Expressing 26 and 91 as product of its prime factors, we get,
26 = 2 × 13 × 1
91 = 7 × 13 × 1
Therefore, LCM (26, 91) = 2 × 7 × 13 × 1 = 182
And HCF (26, 91) = 13
Verification
Now, product of 26 and 91 = 26 × 91 = 2366
And Product of LCM and HCF = 182 × 13 = 2366
Hence, LCM × HCF = product of the 26 and 91.
(ii) 510 and 92
Expressing 510 and 92 as product of its prime factors, we get,
510 = 2 × 3 × 17 × 5 × 1
92 = 2 × 2 × 23 × 1
Therefore, LCM(510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460
And HCF (510, 92) = 2
Verification
Now, product of 510 and 92 = 510 × 92 = 46920
And Product of LCM and HCF = 23460 × 2 = 46920
Hence, LCM × HCF = product of the 510 and 92.
(iii) 336 and 54
Expressing 336 and 54 as product of its prime factors, we get,
336 = 2 × 2 × 2 × 2 × 7 × 3 × 1
54 = 2 × 3 × 3 × 3 × 1
Therefore, LCM(336, 54) = = 3024
And HCF(336, 54) = 2×3 = 6
Verification
Now, product of 336 and 54 = 336 × 54 = 18,144
And Product of LCM and HCF = 3024 × 6 = 18,144
Hence, LCM × HCF = product of the 336 and 54.