Question

How to know when to find hcf and lcm in word problems?

Answer 1

When we have to find lowest common factor then we calculate LCM of that number. When we have to find Highest common factor then we calculate HCF of that number.

Answer 2

Here we will get the idea how to solve the word problems on H.C.F and L.C.M.

1. Find the smallest number which on adding 19 to it is exactly divisible by 28, 36 and 45.

First we find the least common multiple (L.C.M.) of 28, 36 and 45.

Therefore, least common multiple (L.C.M.) of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260

Therefore, the required number = 1260 - 19 = 1241
or
2. Find the number which divides 167 and 95 leaving 5 as remainder.

The number divides 167 and leaves 5 as remainder

Therefore, the number divides 167 - 5 = 162 exactly

The number also divides 95 leaving 5 as remainder

Therefore, the number divides 95 - 5 = 90 exactly

Now we have to find highest common factor (H.C.F.) of 162 and 90
or
3. Find the largest number that divides 92 and 74 leaving 2 as remainder.

The number divides 92 and leaves 2 as remainder

Therefore, the number divides 92 - 2 = 90 exactly

The number also divides 74 leaving 2 as remainder

Therefore, the number divides 74 - 2 = 72 exactly

Now we have to find highest common factor (H.C.F.) of 90 and 72

Highest common factor (H.C.F.) of 90 and 72 = 18

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