the H.C.Of two numbers is 7and their L.C.M is 140.If one of the numbers is 28,find the other number
the two numbers are 7a and 7b
where a & b have no common factors
The LCM is ab/7
So, if 7a=28, 28b/7 = 140
b = 140*7/28 = 20/4 = 5
check: LCM(28,35) = 140
140 = 2*2*5*7
28 = 2*2*7
140/28 = 35 , both 140 and 28 have a factor of 7, but not the 5
So it looks like 35 is the other number.
check:
35 = 5*7
28 = 4*7
Highest common factor is 7
LCM = 5*7*4 = 140
To find the other number, we can use the formula:
H.C.F. × L.C.M = Product of two numbers
Let's substitute the given values into the formula:
H.C.F. = 7
L.C.M. = 140
One of the numbers = 28
So, we have:
7 × 140 = 28 × Other number
Simplifying the equation:
980 = 28 × Other number
To find the other number, divide both sides of the equation by 28:
980 ÷ 28 = Other number
Other number = 35
Therefore, the other number is 35.