Question

1. Find the HCF and LCM of 6,72 and 120, using the Prime factorization method.
2. Find the HCF and LCM of 510 and 92 and also verify it.
3. Explain why 7 x 11 x 13 + 13 is a composite number
DO​

Answer 1

Answer:

Step-by-step explanation:

for 1st,

          6   =2*3

          72 =2*3*2*2*3

          120=2*3*2*2*5

•   lcm=2*3*2*2*3*5=360

•   hcf=2*3*2*2=24

for 2nd,

            HCF of 510 and 92.

510 = 92 x 5 + 50

92 = 50 x 1 + 42

50 = 42 x 1 + 8

42 = 8 x 5 + 2

8 = 2 x 4 + 0

∴ HCF of 510 and 92 = 2

Product of two numbers = Product of their LCM and HCF

510 x 92 = 2 x LCM

LCM = (510 x 92) / 2

       = 23460

∴ LCM of 510 and 92 = 23460.

for 3rd,

           

Answer 2

*Answer*

1.

Ans:- 6 = 2×3

72 = 2×2×2×3×3

120 = 2×2×2×3×5

H.C.F = 2×3

= 6

L.C.M = 2×2×2×3×3×5

=360

2.

Ans:- 510 = 2×3×5×17

92 = 2×2×23

HCF(510,92)=2

LCM(510,92)=2×2×3×5×17×23

= 23460

HCF×LCM=2×23460

=46920

510×92=46920

Hence verified.

3.

And:- 7×11×13+13=13×(7×11+1)

=13×78

=13×13×6

Therefore,

The given expression has 6 and 13 as it's factors. Therefore , it is composite number.