Question: The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, the other number is :
A
215
B
220
C
225
D
235
Note:solution:
Let H.C.F. be h and L.C.M. be l. Then,
`l=45h`
`and l+h=1150`.
`:. 45h+h =1150`
`or h=25`.
`So, l=(1150-25)=1125`.
`:.`other number =`(25 xx 1125)/125 `
`=225`.
Question: The product of two 2-digit numbers is 2028 and their G.C.M. is 13. The numbers are:
A
26,78
B
39,52
C
13,156
D
36,68
Note:solution:
Let the numbers be 13a and 13b.Then,
`13a xx 13b = 2028`
`=> ab = 12`.
Now, co-primes with product 12 are `(1,12) and (3,4)`.
So, the numbers with H.C.F. 13 and product 2028 are:
`(13 xx 1, 13 xx 12) and (13 xx 3, 13 xx 4)`.
`:.` Required 2-digit numbers are `39 & 52`.
Question: About the number of pairs which have 16 as their H.C.F. and 139 as their L.C.M., we can definitely say that :
A
only one such pair exists
B
only two such pairs exist
C
many such pairs exist
D
no such pair exists
Note:solution:
H.C.M. of two numbers divides their L.C.M. exactly.
Since 16 is not a factor of 136, it follows that there does not exist any pair of numbers with H.C.F. 16 and L.C.M. 136.
Question: The H.C.F. and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is:
A
50
B
100
C
125
D
250
Note:solution:
First number =(50`xx`2) = 100.
Second number =`((50xx250)/100)` = 125.