Question

Find the LCM and HCF of 5 10 and 92 and
check whether LCM × HCF = product of the
given numbers.​

Answer 1

Step-by-step explanation:

⭐Question:-

Find the LCM and HCF of 5 10 and 92 and check

whether LCM × HCF = product of the

⭐Answer:-

The Highest Common Factor (HCF)

is the largest common divisor or

gcd of two or more positive

integers, as the mathematics rules dictate, appears to be the largest positive integer that divides the numbers without leaving a remainder.

✪Example:

Consider the two number 8 and 12.

As the highest number that can

divide both 8 and 12 is 4.

Therefore, the H.C.F. of 8 and 12 would be 4.

In arithmetic, Least common multiple LCM (a,b)

is the least common multiple of tw

o numbers, a and b. And the LCM is the smallest or least positive integer that is divisible by both a and b.

✪Example:

Consider the two number 8 and 12 and let us

write the multiples of two numbers.

Multiples of 8 = 16, 24, 32, 40 ,48, 56……

Multiples of 12 = 24, 36, 48, 60, 72………

From the above list, we can observe that least common multiples of 8

and 12 is 24.

I.e LCM (8, 12) = 24

Let us find the HCF of 510 and 92.

510 = 2×5×3×17

92 = 2×2×23

∴ HCF (510, 92) = 2

Let us find the LCM of 510 and 92.

LCM(510,92) = 2×2×3×5×17×23

∴ LCM(510,92) =23,460

Let us verify LCM and HCF is equals to the product of two numbers

LCM × HCF = 510 × 92

23,460 × 2 = 510 × 92

46,920 = 46,920

✿Hence, L.H.S. = R.H S. (proved)