Question

1) the HCF of two numbers 525 and 1155 is 105 find their LCM

2) the LCM of two numbers 660 and 2100 is 23100 find their HCF


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Answer 1

Answer:

1) the LCM of two numbers 525 and 1155 is 5775.

2) the HCF of two numbers 660 and 2100 is 60.

Answer 2

Concept

The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF).

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

The relationship between any two numbers, a and b, and their Highest Common Factor (HCF) and Least Common Multiple (LCM) is stated as:

$\[a\times b=HCF\left( a,b \right)\times LCM\left( a,b \right)\]$

Given

The Highest Common Factor (HCF) of the two numbers is $105$ and the two numbers are $525$ and $1155$.

Find

We have to find the Least Common Multiple (LCM) of the two numbers.

Solution

Consider the two numbers be $\[a\text{ }and\text{ }b\]$, then

$\[a\times b=525\times 1155$

The value of Highest Common Factor (HCF) is $105$, i.e.

$\[HCF\left( a,b \right)=105\]$

Now, using  $\[a\times b=HCF\left( a,b \right)\times LCM\left( a,b \right)\]$, we get

$\[525\times 1155=105\times LCM\left( a,b \right)\]$

$\[LCM\left( a,b \right)=\frac{525\times 1155}{105}\]$

$\[LCM\left( a,b \right)=5775\]$

Hence, $5775$ is the required Least Common Multiple (LCM) of the two numbers.

#SPJ2

Concept

The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF).

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

The relationship between any two numbers, a and b, and their Highest Common Factor (HCF) and Least Common Multiple (LCM) is stated as:

$\[a\times b=HCF\left( a,b \right)\times LCM\left( a,b \right)\]$

Given

The Least Common Multiple (LCM) of the two numbers is $660$ and the two numbers are $2100$ and $23100$.

Find

We have to find the Highest Common Factor (HCF) of the two numbers.

Solution

Consider the two numbers be $\[a\text{ }and\text{ }b\]$, then

$\[a\times b=2100\times 23100$

The value of Least Common Multiple (LCM) is $660$, i.e.

$\[LCM\left( a,b \right)=660\]$

Now, using  $\[a\times b=HCF\left( a,b \right)\times LCM\left( a,b \right)\]$, we get

$\[2100\times 23100= HCF\left( a,b \right)\]\times660$

$\[HCF\left( a,b \right)=\frac{2100\times 23100}{660}\]$

$\[LCM\left( a,b \right)=73500\]$

Hence, $73500$ is the required Highest Common Factor (HCF) of the two numbers.

#SPJ2