2. Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF=product of the two numbers.
(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
(i) 26 and 91
HCF=Product of the smallest power of each common prime factor in the numbers=13
LCM=Product of the greatest power of each prime factor involved in the numbers
HCF
LCM
Product of two given numbers=
Therefore, it is proved that LCM
HCF=product of two numbers
(ii) 510 and 92
HCF=Product of the smallest power of each common prime factor in the numbers=2
LCM=Product of the greatest power of each prime factor involved in the numbers
LCM
HCF
Product of two given numbers
Therefore, it is proved that LCM
HCF=product of two given numbers.
(iii) 336 and 54
HCF=Product of the smallest power of each common prime factor in the numbers
LCM=Product of the greatest power of each prime factor involved in the numbers
HCF
LCM=
Product of two given numbers
Therefore, it is proved that LCM
HCF =product of two given numbers.
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