The L.C.M. of two numbers is 4800 and their G.C.M. is 160. If one of the…

To find the missing number, you can use the fundamental property relating the Greatest Common Measure (G.C.M.), also known as the Greatest Common Divisor (G.C.D.), and the Least Common Multiple (L.C.M.) of two numbers.

The Property
For any two numbers, the product of the numbers is equal to the product of their G.C.M. and L.C.M.:
First Number * Second Number = G.C.M. * L.C.M.

Step-by-Step Calculation
Identify the given values:

L.C.M. = 4800

G.C.M. = 160

First Number = 480

Second Number = ? (Let's call it x)

Set up the equation:
480 * x = 160 * 4800

Solve for x:

x = (160 * 4800) / 480

Simplifying the fraction (4800 / 480 = 10):

x = 160 * 10

x = 1600