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Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. 26 and 91

 Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
 
26 and 91

Grade:12

3 Answers

Harshit Singh
askIITians Faculty 5965 Points
one year ago
Dear Student

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= 2366

And Product of LCM and HCF = 182 × 13 = 2366

Hence, Proved

Thanks
KRIPA SHANKAR DWIVEDI
18 Points
9 months ago
Prime factors of 26 and 91 
26=2×13×1
91=7×13×1
Hence H.C.F=13
L.C.M=2×7×13×1=182
Now we have to verify that 
H.C.F×L.C.M=Product of two numbers
LHS-
H.C.F×L.C.M
13×182
2366
RHS-
Product of two numbers
26×91
2366
Hence 
LHS=RHS
Hence verified
                 
Ram Kushwah
110 Points
9 months ago
The given numbers are 26 and 91
Let a= 26 and b=91
The prime factors of 26 and 91 are
26= 2 x 13
91 = 7 x 13
So we get 
 HCF= 13
 and LCM = 2 x 7 x13
=14 x 13
= 182
Now  HCF x LCM =182 x 13
=(2 x 7 x 13) ( 13)
=(2 x13) ( 7x13)
=26 x  91
= a x b
hence we get
HCF x LCM = a x b
hence proved

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