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Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF-product of the two numbers.0 26 and 91310 and 92(i) 336 and 54 |
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Answer» 26 = 2 x 1391=7 x 13HCF = 13LCM =2 x 7 x 13 =182Product of two value 26 x 91 = 2366Product of HCF and LCM 13 x 182 = 2366 ii. 510 = 2 x 3 x 5 x 1792 =2 x 2 x 23HCF =2 LCM =2 x 2 x3 x 5 x 17 x 23 = 23460Product of both values 510x92 = 46920Product of HCF and LCM 2x23460 =46920Hence, product of two numbers = product of HCF × LCM. Let a = 336 , b = 54 Expressing a and b as a product of prime factors 336 = 2 × 2 × 2× 2 × 3 × 7 = 2^4 × 3 × 7 54 = 2 × 3 × 3 × 3 = 2 × 3^3 HCF ( 336 , 54 ) = 2 × 3 = 6 LCF( 336 , 54 ) = 2^4 × 3^3 × 7 = 3024 We know that ,_____________________________ For any two positive integers a and b . HCF( a , b ) × LCM( a , b ) = a × b Verification : HCF( 336 , 54 ) × LCM( 336 , 54 ) = 6 ×3024= 18144 -----( 1 )a × b = 336 × 54 = 18144 ----( 2 ) Therefore ,( 1 ) = ( 2 ) thanks for all answers |
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