Question

which two consecutive even number have an LCM of 180​

Answer 1

Answer:

Let the required numbers be; n and (n+1)

then,

Their HCF=1.

{ HCF of two consecutive numbers is always 1.}

Also, it is given that,

their LCM=180.

now, we know that,

product of two numbers= product of their HCF and LCM.

thus ,we have;

=> n(n+1)=1x180

=> n^2+n=180

=> n^2+n-180=0

here , it can't be resolved in factors to get natural value of n.

so there exist no pairof natural numbers whose LCM is 180.

moreover, if we find the value of n using quadratic formula, then we would get irrational numbers.

so we can say that , no pair of consecutive natural numbers has their LCM as 180.

I hope it would help you

thank you