What least number must be subtracted from 2469 to make it exactly divisible by 65?
Answers
Step-by-step explanation:
on
Answers
Related Questions
The least number which should be added to 2497
so that the sum is exactly divisible by 5,6,4,3
is
(a) 3
(b) 13
(c) 23
(d) 33
Answer
VerifiedVerified
67.2k+ views
8.4k+ likes
Hint:
This problem is based on the concept of L.C.M. of numbers. First find the L.C.M. of the given numbers by which the sum should be exactly divisible. Then divide the number 2497
by this L.C.M. the remainder obtained from this division needs to be subtracted from the L.C.M. to get the least number that needs to be added.
Complete step by step solution:
Before proceeding with the problem we first need to know that the L.C.M. of two numbers is the smallest number that is completely divisible by both the numbers.
Here we need to find the least number that needs to be added to 2497
such that the sum is divisible exactly by 5,6,4,3
. Now for the sum to be divisible by all the given numbers it has to be divisible by the L.C.M. of these numbers. Let us first find the L.C.M. of the given numbers.
We’ll find the L.C.M. by the division method:
2∣∣5,6,4,3−−−−−−−3∣∣5,3,2,3−−−−−−−∣∣5,1,2,1−−−−−−−
Therefore L.C.M. =
2×3×5×1×2×1
.
=60
Next divide the number 2497
by 60
. Doing so we obtain a quotient of 41
and a remainder of 37
. So 2497
is not completely divisible by 60
, but if the difference: (60−37)
, i.e. 23
is added to 2497
, then it will be completely divisible by 60
and will be exactly divisible by 5,6,4,3
.
Hence the least number to be added to 2497
to make it divisible exactly by 5,6,4,3
is 23
.
Correct option is (c).
Note:
L.C.M. means the lowest common multiple. Alternatively the L.C.M. of the numbers can also be found by the prime factorization method. In the prime factorization method first we need to find the prime factors of each number. Then the L.C.M. will be the product of all prime factors with the highest degree (power).
67.2k+ views
8.4k+ likes
Related Questions
The value of (0.1)2+(0.01)2+(0.009)2(0.01)2+(0.001)2+(0.0009)2−−−−−−−−−−−−−−−−−−−−−−−−⎷
If the HCF of 65 and 117 is expressible in the form 65n−117
. Find the value of n?