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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 1. 26and91 2.510and92?
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Find the LCM and HCF of the following pairs of integers and verify tha...
Pair 1: 26 and 91

Finding HCF (GCD)
To find the HCF (GCD) of 26 and 91, we can use the Euclidean algorithm:

91 = 3 × 26 + 13
26 = 2 × 13 + 0

Since the remainder is 0, the HCF is the last non-zero number we obtained, which is 13.

Finding LCM
To find the LCM of 26 and 91, we can use the formula LCM(a, b) = (a × b) / HCF(a, b):

LCM(26, 91) = (26 × 91) / 13 = 182

Verification
Now, we can verify that LCM × HCF = product of the two numbers:

LHS = LCM × HCF = 182 × 13 = 2366
RHS = product of the two numbers = 26 × 91 = 2366

Since LHS = RHS, we have verified that LCM × HCF = product of the two numbers.

Pair 2: 510 and 92

Finding HCF (GCD)
To find the HCF (GCD) of 510 and 92, we can use the Euclidean algorithm:

510 = 5 × 92 + 30
92 = 3 × 30 + 2
30 = 15 × 2 + 0

Since the remainder is 0, the HCF is the last non-zero number we obtained, which is 2.

Finding LCM
To find the LCM of 510 and 92, we can use the formula LCM(a, b) = (a × b) / HCF(a, b):

LCM(510, 92) = (510 × 92) / 2 = 23460

Verification
Now, we can verify that LCM × HCF = product of the two numbers:

LHS = LCM × HCF = 23460 × 2 = 46920
RHS = product of the two numbers = 510 × 92 = 46920

Since LHS = RHS, we have verified that LCM × HCF = product of the two numbers.
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Find the LCM and HCF of the following pairs of integers and verify tha...
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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 1. 26and91 2.510and92?
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