Question

Find the least number which when divided by 48,60,72,108and 140 leaves 38,50,62,98 and 130 as remainders respectively .

Answer 1

Answer:

Factors of 48,60,72,108 and 140 are:

48=2^4*3

60=2^2*3*5

72=2^3*3^2

108=2^2*3^3

140=2^2*5*7

SO LCM (48,60,72,108,140)=2^4 * 3^3*5*7

=16*27*5*7=15120

Now each time remainder=divisor-10

Let the No=N,quotient=q and remainder=R,divisor=d

Now each time remainder R=d-10——————-(1)

LCM=dq

this can be written as

LCM-10=d(q-1)+d-10——————-(2)

we know that

N=quotient*divisor+R—————-(3)

Comparing (2) and (3) we get

N=LCM-10

=15120–10=15110

The said number=15110