Question

15) Consider the conditions about the numbers m and n:

Condition 1: both are 2-digits numbers
Condition 2: one is add and one is even if m x n=180, what is the smallest common
multiple of m and n?
a)60
b)90
c)180
d)36

Answer 1

The smallest common multiple of m and n is 60.

The correct option is (a) 60.

Step-by-step explanation:

We are given two conditions about two numbers m and n:

1. Both numbers are 2-digit numbers.
2. One number is odd and the other number is even.

We are also given that the product of m and n is 180.

We need to find the smallest common multiple of m and n.

Let's first find the factors of 180.

• 1 x 180 = 180
• 2 x 90 = 180
• 3 x 60 = 180
• 4 x 45 = 180
• 5 x 36 = 180
• 6 x 30 = 180
• 9 x 20 = 180
• 10 x 18 = 180

Out of these factor pairs, we need to find the pair that satisfies the given conditions.

Since one number is odd and the other number is even, we can eliminate the factor pairs (2, 90), (4, 45), (6, 30), and (10, 18).

Now, we are left with the factor pairs (1, 180), (3, 60), and (9, 20).

Since both numbers are 2-digit numbers, we can eliminate the factor pair (1, 180).

Out of the remaining factor pairs, (3, 60) and (9, 20), we need to find the smallest common multiple.

The smallest common multiple of two numbers is the product of the two numbers divided by their greatest common divisor (GCD).

The GCD of 3 and 60 is 3, and the GCD of 9 and 20 is 1.

Therefore, the smallest common multiple of m and n is:

For the pair (3, 60): (3 x 60) / 3 = 60

For the pair (9, 20): (9 x 20) / 1 = 180

Thus, the smallest common multiple of m and n is 60.

Answer 2

a

Step-by-step explanation:

Note that m and n are 2 digit numbers. Let m be even and n be odd. The product of these numbers is 180.

Notice that:

`180=12* 15`

So,
`m=12` and
`n=15`. Then, the lowest common multiple of
`m=12` and
`n=15` is 60.