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HomeMathRelationship between H.C.F. and L.C.M. |Highest Frequent Issue|Examples

Relationship between H.C.F. and L.C.M. |Highest Frequent Issue|Examples


We are going to be taught the connection between H.C.F. and L.C.M. of
two numbers.

First we have to discover the very best frequent issue (H.C.F.) of 15 and 18 which is 3.

Then we have to discover the bottom frequent a number of (L.C.M.) of 15 and 18 which is 90.

H.C.F. × L.C.M. = 3 × 90 = 270

Additionally the product of numbers = 15 × 18 = 270

Subsequently, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18.


Once more, allow us to think about the 2 numbers 16 and 24

Prime components of 16 and 24 are:

         16 = 2 × 2 × 2 × 2

         24 = 2 × 2 × 2 × 3

L.C.M. of 16 and 24 is 48;

H.C.F. of 16 and 24 is 8;

L.C.M. × H.C.F. = 48 × 8 = 384

Product of numbers = 16 × 24 = 384

So, from the above explanations we conclude that the product of highest frequent issue (H.C.F.) and lowest frequent a number of (L.C.M.) of two numbers is the same as the product of two numbers

or, H.C.F. × L.C.M. = First quantity × Second quantity

or, L.C.M. = (frac{textrm{First Quantity} instances textrm{Second Quantity}}{textrm{H.C.F.}})

or, L.C.M. × H.C.F. = Product of two given numbers

or, L.C.M. = (frac{textrm{Product of Two Given Numbers}}{textrm{H.C.F.}})

or, H.C.F. = (frac{textrm{Product of Two Given Numbers}}{textrm{L.C.M.}})

Solved examples on the
relationship between H.C.F. and L.C.M.:

1. Discover the
L.C.M. of 1683 and 1584.

Answer:

First we discover highest frequent
issue of 1683 and 1584                      

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

Subsequently, highest frequent issue of 1683 and 1584 = 99

Lowest frequent a number of of 1683 and 1584 = First quantity ×
Second quantity/ H.C.F.

                                                               = (frac{1584 × 1683}{99})

                                                               = 26928

2. Highest frequent
issue and lowest frequent a number of of two numbers are 18 and 1782 respectively.
One quantity is 162, discover the opposite.

Answer:

We all know, H.C.F. × L.C.M. = First quantity × Second quantity then
we get,

18 × 1782 = 162 × Second quantity

(frac{18 × 1782}{162}) = Second quantity

Subsequently, the second quantity = 198

3. The HCF of two numbers is 3 and their LCM is 54. If one among
the numbers is 27, discover the opposite quantity.

Answer:

HCF × LCM = Product of two numbers

3 × 54 = 27 × second quantity

Second quantity = (frac{3 × 54}{27})

Second quantity = 6

Relation Between HCF and LCM

4. The best frequent issue and the bottom frequent a number of of two numbers are 825 and 25 respectively. If one of many two numbers is 275, discover the opposite quantity.

Answer:

We all know, H.C.F. × L.C.M. = First quantity × Second quantity then we get,

                        825 × 25 = 275 × Second quantity

                (frac{825 × 25}{275}) = Second quantity

Subsequently, the second quantity = 75

5. Discover the H.C.F. and L.C.M. of 36 and 48.

Answer:

H.C.F. = 2 × 2 × 3 = 12

L.C.M. = 2 × 2 × 3 × 3 × 4 = 144

H.C.F. × L.C.M. = 12 × 144 = 1728

Product of the numbers = 36 × 48 = 1728

Subsequently, product of the 2 numbers = H.C.F × L.C.M.

2. The H.C.F. of two numbers 30 and 42 is 6. Discover the L.C.M.

Answer:

We’ve got H.C.F. × L.C.M. = product of the numbers

6 × L.C.M. = 30 × 42

L.C.M. = [frac{30 × 42}{sqrt{6}}]

          = [frac{1260}{sqrt{6}}]

          = 210

3. Discover the best quantity which divides 105 and 1800 fully.

Answer:

The best quantity right here is the H.C.F of 105 and 180

Frequent components are 5, 3

H.C.F. = 5 × 3 = 15

Subsequently, the best quantity that divides 105 and 180 fully is 15.

4. Discover the least quantity which leaves 3 as the rest when divided by 24 and 42.

Answer:

L.C.M. = 2 × 3 × 4 × 7 = 168

The least quantity which leaves 3 as the rest is 168 + 3 = 171.

Necessary Notes:

Two numbers which have only one because the frequent issue are referred to as co-prime.

The least frequent a number of (L.C.M.) of two or extra numbers is the smallest quantity which is divisible by all of the numbers.

If two numbers are co-prime, their L.C.M. is the product of the numbers.

If one quantity is the a number of of the opposite, then the a number of is their L.C.M.

L.C.M. of two or extra numbers can’t be lower than any one of many given numbers.

H.C.F. of two or extra numbers is the very best quantity that may divide the numbers with out leaving any the rest.

If one quantity is an element of the second quantity then the smaller quantity is the H.C.F. of the 2 given numbers.

The product of L.C.M. and H.C.F. of two numbers is the same as the product of the 2 given numbers.

Questions and Solutions on Relationship between H.C.F. and L.C.M.

1. The H.C.F. of two numbers 20 and 75 is 5. Discover their L.C.M.

2. The L.C.M. of two numbers 72 and 180 is 360. Discover their H.C.F.

3. The L.C.M. of two numbers is 120. If the product of the numbers is 1440, discover the H.C.F.

4. Discover the least quantity which leaves 5 as the rest when divided by 36 and 54.

5. The product of two numbers is 384. If their H.C.F. is 8, discover the L.C.M.

Reply:

1. 300

2. 36

3. 12

4. 113

5. 48

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