Question

Find the HCF and LCM of the numbers given below. Verify that their product is equal to the product of the given number

32,37

46,51

15,60

18,63

78,104

Answer 1

given

$\Rightarrow$ $32,37$

$32=2^5\times 1$ $37=37\times 1$

HCF$=1$

LCM$=2^5\times 37=32\times 37$

$\therefore$ Product of number $=$ product of HCF and LCM

$\Rightarrow$ $46,51$

$\Rightarrow$ $46=2\times 23\times 1$ $51=3\times 17\times 1$

HCF$=1$

LCM$=46\times 51$

$\therefore$ Product of number $=$ product of HCF and LCM

$\Rightarrow$ $15,60$

$\Rightarrow$ $15=3\times 5$ $60=2^2\times 3\times 5$

HCF$=3\times 5=15$

LCM$=3\times 5\times 2^2=60$

$\therefore$ product of number $=$ product of HCF and LCM

$\Rightarrow$ $18,63$

$\Rightarrow$ $18=3^3\times 2$ $63=3^2\times 7$

HCF$=3^2=9$ LCM$=3^2\times 2\times 7=126$

$\therefore$ product of number $=$ product of HCF and LCM

$\Rightarrow$ $78,104$

$78=2\times 3\times 13$ $104=2^3\times 13$

HCF$2\times 13-26$ LCM$=13\times 3\times 2^3$

$\therefore$ product of number $=$ product of HCF and LCM