Question

The Icm of two coprime number is 420 . If one of them is 28,find the other​

Answer 1

Given :–

• The L.C.M. (least common multiple) of two co-prime = 420.
• One of the number = 28.

To Find :–

• The other number.

Solution :–

Let,

The other number be $\beta$.

We know that,

L.C.M. (least common multiple) of two co-prime numbers is their product.

• L.C.M. of two co-prime numbers = 420

It means,

→ $\alpha \times \beta = 420$

→ $\alpha = 28$

Now, put the value.

→ $28 \times \beta = 420$

→ $\beta = \dfrac{ \cancel{420}}{ \cancel{28}}$

→ $\beta = \dfrac{ \cancel{210}}{ \cancel{14}}$

→ $\beta = \dfrac{ \cancel{105}}{ \cancel{7}}$

→ $\beta = 15$

Hence,

The other number is 15.

Check :–

L.C.M. is in the attachment.

L.C.M. of 28 and 15 = 2 × 2 × 3 × 5 × 7

→ 2² × 3 × 5 × 7

→ 4 × 15 × 7

→28 × 15

→ 420

We get 420 as the L.C.M. of two co-primes (28 and 15)

So, the other number = 15 is correct.

Answer 2

Answer:

Given :–

The L.C.M. (least common multiple) of two co-prime = 420.

One of the number = 28.

To Find :–

The other number.

Solution :–

Let,

The other number be \betaβ .

We know that,

L.C.M. (least common multiple) of two co-prime numbers is their product.

L.C.M. of two co-prime