LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RELATION BETWEEN HCF & LCM

__Relation between HCF & LCM __

**HCF X LCM = First
Number X Second Entertainment**

**From the above equation, we can conclude that, the product of two numbers is equal to the product of their HCF
& LCM and the **

**HCF of the two
numbers can’t be greater than any of the given numbers.**

**HCF of two co-prime
numbers = 1**

**The LCM of two
co-prime numbers = the product of the numbers **

**LCM of two numbers
cannot be less than any of the given numbers**

__Example
– 1__

**The LCM
& HCF of the two numbers is 336 & 28 respectively. If one
number is 112 then find out the other number**

**Ans.) As per the
given condition formula is HCF X LCM = First Number X Second Entertainment**

**
HCF X LCM **

**So, Required number =
---------------**

**
Given number**

**
336 X 28**

**So, Required number
= ----------------- = 84 (Ans.)**

**
112**

__Example.– 2__

**If the
product of two number is 23814 and their LCM is 378 then find their HCF**

**Ans.) as per the
given condition –**

**1 ^{st} Number
X 2^{nd} Number = HCF X LCM**

**
1 ^{st} Number X 2^{nd}
Number 23814**

**=> HCF
= ------------------------ = ----------- = 63**

** LCM
378**

**So, the required LCM
is 63**

__Example– 3__

**Find
the smallest number which when divided by 25, 40, 80, 120 leaves the
remainder 11 in each case.**

**Ans.) The smallest
number divisible by 25, 40, 80, 120 = the LCM of 25, 40, 80, 120. **

**So, LCM of the
numbers 25, 40, 80, 120 is 5 X 4 X 2 X 5 X 2 X 3 X 1 = 1200**

**So, as per the given
condition the required number must be = obtained LCM from given numbers +
11 = 1200 + 11 = 1211 (Ans.)**

__Example-
4__

**Find
the greatest number of 6 digits which is exactly divisible by 10, 20,
25, 35, 40.**

**First, we have to find
LCM of 10, 20, 25, 35, 40 **

**So, the LCM of
10, 20, 25, 35, 40 = 5 X 2 X 2 X 5 X 7 X 2 = 1400**

**The greatest six-digit number is = 999999. Let us see if it is a multiple of 1400**

**Consider 1400 as divisor and 999999 as dividend.**

**Here the remainder is
399. So, the number would be 999999 – 399 = 999600
(Ans.)**

__Example– 5__

**Find the smallest number of six digits which is exactly divisible by 10, 20, 25, 35, 40.**

**First, we have to find
LCM of 10, 20, 25 , 35, 40 **

**So, the LCM of
10, 20, 25, 35, 40 = 5 X 2 X 2 X 5 X 7 X 2 = 1400**

**The smallest six-digit number is = 100000. **

**Let us see if it is a
multiple of 1400.**

**Consider 1400 as
divisor and 100000 as dividend**

**So, the required
numbers = **

** 100000 – Remainder + LCM **

** = 100000 – 600 + 1400**

**
**

** = 100800 (Ans.)**