Word problems on H.C.F. and L.C.M.

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

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

Highest common factor (H.C.F.) of 90 and 162 = 18

Therefore, 18 is the required number.

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

Therefore, 18 is the required number.

● Multiples.

Common Multiples.

Least Common Multiple (L.C.M).

To find Least Common Multiple by using Prime Factorization Method.

Examples to find Least Common Multiple by using Prime Factorization Method.

To Find Lowest Common Multiple by using Division Method

Examples to find Least Common Multiple of two numbers by using Division Method

Examples to find Least Common Multiple of three numbers by using Division Method

Relationship between H.C.F. and L.C.M.

Worksheet on H.C.F. and L.C.M.

Word problems on H.C.F. and L.C.M.

Worksheet on word problems on H.C.F. and L.C.M.

5th Grade Math Problems 

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