# Will there be 'Highest Common Multiple' and the 'Lowest Common Factor'? If yes, what will be there usage?

**HI,**

**H.C.F.** means Highest Common Factor i.e. the factor which is common in the given numbers.

Suppose you have to find the H.C.F. of 42 and 54,then

We can write 42=2×3×7 and 54=2×3×3×3

Clearly, 2 and 3 are common in prime factorization of both 42 and 54.

Hence the H.C.F. of 42 and 54 is 2×3= 6

**L.C.M. **Least Common Multiplier i.e. the smallest number which is divisible by the given numbers.

Suppose the given numbers are 21, 32, 43.

21=3×7

32=2×2×2×2×2

43=1×43

The L.C.M. of 21, 32 and 43 = 2×2×2×2×2×3×7×43=28896

**H.C.F. : We use H.C.F. method where we need :**

1) To split things into smaller sections?

2) To equally distribute 2 or more sets of items into their largest grouping?

3) To figure out how many people we can invite?

4) To arrange something into rows or groups?

**Real life example :**Priyanka has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?

**Answer:**

This problem can be solved using H.C.F. because we are cutting or “dividing” the strips of cloth into smaller pieces (Factor) of 72 and 90 (Common) and we are looking for the widest possible strips (Highest).

So,

H.C.F. of 72 and 90 is 18

So we can say that

Priyanka should cut each piece to be 18 inches wide .

**L.C.M. : we use find L.C.M. where ,**

1) About an event that is or will be repeating over and over.

2) To purchase or get multiple items in order to have enough.

3) To figure out when something will happen again at the same time.

**Real life example :**Ram exercises every 12 days and Deepika every 8 days. Ram and Deepika both exercised today. How many days will it be until they exercise together again?

So,

This problem can be solved using Least Common Multiple because we are trying to figure out when the soonest (Least) time will be that as the event of exercising continues (Multiple), it will occur at the same time (Common).

Answer : L.C.M. of 12 and 8 is 24 .

SO,

They will exercise together again in 24 days.

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