Question

Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
A. 24
B. 25
C. 26
D. 27

Answer 1

lcm × gcf = 16 × N
48 × 8 = 16 × N
N = (8 × 48)/16
= 24


hence, N = 24

Answer 2

The second number is 24.

Explanation-

Given-Two numbers N and 16 have LCM = 48 and GCF = 8.

Find N.

Solution-

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm, is the smallest positive integer that is divisible by both a and b.

The HCF (Highest Common Factor) of two numbers is the highest number among all the common factors of the given numbers. For example, the HCF of 12 and 36 is 12 because 12 is the highest common factor of 12 and 36.

According to the question,

The product of two numbers which is equal to the product pf LCM and HCF.

So,

$N\times 16=HCF\times LCM$

$N\times 16=48 \times 8$

$N\times =\frac{48\times 8}{16}$

$N=24$

The second number is 24.

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