Question

the product of two numbers is 750 and their hcf is 5 find their lcm?
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Answer 1

Step-by-step explanation:

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Related Questions

The product of two numbers is 750 and the H.C.F. is 5. Find the L.C.M.

Answer

Hint: Here, we need to find the L.C.M. of the two numbers. We will use the property of the product of H.C.F. and L.C.M. of two numbers to form an equation. Then, we will simplify the equation to find the L.C.M. of the two numbers.

Complete step-by-step answer:

Let the two numbers be a

and b

.

It is given that the product of the two numbers is 750.

Therefore, we get

a×b=750

The H.C.F. of the two numbers a

and b

is given by H.C.F.(a,b)

.

It is given that the H.C.F. of the two numbers is 5.

Therefore, we get

H.C.F.(a,b)=5

The L.C.M. of the two numbers a

and b

is given by L.C.M.(a,b)

.

The product of the H.C.F. and L.C.M. of two numbers a

and b

is equal to the product of the two numbers a

and b

.

Thus, we get the equation

H.C.F.(a,b)×L.C.M.(a,b)=a×b

Substituting H.C.F.(a,b)=5

and a×b=750

in the equation, we get

⇒5×L.C.M.(a,b)=750

This is a linear equation. We will simplify this linear equation to find the value of the L.C.M.

Dividing both sides of the equation by 5, we get

⇒5×L.C.M.(a,b)5=7505

Simplifying the expression, we get

∴L.C.M.(a,b)=150

Therefore, we get the L.C.M. of the two numbers as 150.