Question

find LCM & HCF of 40, 36 and 126 by prime factorization method. Show that HCF × LCM not equal to product of numbers.

Answer 1

40 =2*2*2*5
36= 2*2*3*3
126 = 2*3*3*7

hcf(40,36,126)=2

lcm = 2*2*2*5*2*3*3*3*3*7=45360

hcf*lcm=2*45360=90720---(1)

product of the numbers= 40*36*126=181440----(2)


(1) ≠(2)

Answer 2

LCM is 2520 and HCF is 2

Step-by-step explanation:  

LCM is the least common multiple that divides all the three numbers.

$L C M=2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7=2520$

HCF is the highest common divisor that divides all the three numbers.

$40=2 \times 2 \times 2 \times 5; \ \ 36=2 \times 2 \times 3 \times 3; \ \ 126=2 \times 3 \times 3 \times 7$

Therefore HCF = 2

$L C M \times H C F=2520 \times 2=5040$

$\text{Product of three numbers} =40 \times 36 \times 126=181440$

Hence, Product of three numbers is not equal to LCM $\times$ HCF.