Question

Find LCM and HCF of the following pairs of integers and verify that LCM X HCF = product of two numbers.686 and 735

Answer 1

Answer:

the prime factorisation of 686 is 2 x 7 x 7 x 7

&

the prime factorisation of 735 is 3 x 5 x 7 x 7

Then The HCF is = 7 × 7 (common in both) = 49

&

The LCM is = 2 x 3 x 5 x 7 x 7 x 7 ( take only one no. from the common and rest other as well) = 10,290

Verification

1st Number × 2nd Number = LCM × HCF

686 × 735 = 10,290 × 49

504210 = 504210

LHS = RHS (hence proved)

Answer 2

Given :  two numbers.686 and 735

To find : LCM & HCF of  686 and 735

Solution:

 686

735

686  = 2  * 7 * 7 * 7

735 = 3 * 5  * 7 * 7

HCF  = Highest Common Factor  

HCF =  7 * 7  = 49

LCM = Least Common Multiplier

LCM = 2 * 3 * 5 * 7 * 7  * 7

LCM = 10290

LCM * HCF =  49 * 10290 = 504210

686 * 735  = = 504210

504210 = 504210

LCM * HCF = Number 1 *  Number 2

LCM = 10290

HCF =  49

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