Question

Find the HCF and LCM of the pairs of integers and verify that $LCM(a,b)\times HCF(a,b)=a\times b$ for $125$ and $55$

Answer 1

The given integers $125$ and $55$ can be factorised as follows:

$125=5\times 5\times 555=5\times 11$

$5$ and $11$ are prime numbers as these are the numbers that are only divisible by themselves.

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $125$ and $55$ is:

$HCF=5$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $125$ and $55$ is:

$LCM=5\times 5\times 11=1375$

Therefore, the $HCF$ is $5$ and $LCM$ is $1375$.

Now, let $a=125$ and $b=55$, then the product of $a$ and $b$ is:

$a\times b=125\times 55=\mathrm{6875.......}\left(1\right)$

Also, the product of the $LCM$ and $HCF$ of $a$ and $b$ is:

$LCM(a,b)\times HCF(a,b)=1375\times 5=\mathrm{6875.......}\left(2\right)$

Hence, from equations 1 and 2, we get $LCM(a,b)\times HCF(a,b)=a\times b$.