Question

find HCF and LCM of 240 and 6552 and verify the relation between HCF and LCM



PLZZ answer this question guys ​

Answer 1

Answer:

We find HCF using Euclid division algorithm

Euclid division algorithm states that given no. will be written in form of

a = bq + r where q is quotient , b is divisor and r is remainder

if r ≠ 0

then q become dividend and r become divisor

again we write in form of a = bq + r

this procedure is followed until r = 0 comes.

then HCF = b

So,

6552 = 240 × 27 + 72

240 = 72 × 3 + 24

72 = 24 × 3 + 0

So, we get r = 0

⇒ HCF = 24

Therefore, HCF of 240 and 6552 is 24

HCF of 240 and 6552 is 24

LCM -

Find the prime factorization of 240

240 = 2 × 2 × 2 × 2 × 3 × 5

Find the prime factorization of 6552

6552 = 2 × 2 × 2 × 3 × 3 × 7 × 13

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13

LCM = 65520

So there is an interesting co-relation between H.C.F and L.C.M. of two numbers. The product of the H.C.F. and L.C.M. of any two numbers is always equal to the product of those two numbers. However the same is not applicable to three or more numbers.