Question

Find the least number which when divided by 25,20 and 24 will leave a remainder of 7 in each case .​

Answer 1

Question :- Find the least number which when divided by 25,20 and 24 will leave a remainder of 7 in each case . ?

Concept :-

• The Least Number which when divided by a, b & c will leave a same remainder of k in each case is given by :- ( LCM of a, b & c) + k (Remainder) .

Solution :-

Lets Find LCM of 25, 20 & 24 first.

Prime - Factors of 25, 20 & 24 :-

→ 25 = 5 * 5 = 5²

→ 20 = 2 * 2 * 5 = 2² * 5

→ 24 = 2 * 2 * 2 * 3 = 2³ * 3

LCM = 5² * 2³ * 3 = 25 * 8 * 3 = 600.

Now, we have given Remainder in each case is 7 = k.

Hence,

→ Least Required Number will be = LCM + k = 600 + 7 = 607 (Ans.)

____________________

★★Extra Brainly Knowledge★★

✯✯ Some Properties of HCF & LCM ✯✯

☛ HCF(Highest Common Factor) :- The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. Also known as GCD (Greatest Common Divisor).

☛ LCM(Least Common Multiple) :- The least or smallest common multiple of any two or more given natural numbers are termed as LCM.

☛ The H.C.F. of given numbers is not greater than any of the numbers.

☛ The L.C.M. of given numbers is not less than any of the given numbers.

☛ The H.C.F. of two co-prime numbers is 1.

☛ The L.C.M. of two or more co-prime numbers is equal to their product.

☛ If a number, say x, is a factor of another number, say y, then the H.C.F. of x and y is x and their L.C.M. is y.

☛ The product of the H.C.F. and the L.C.M. of two numbers is equal to the product of the given numbers. That is, if a and b are two numbers, then a x b = H.C.F. x L.C.M.

☛ LCM of fractions = ( LCM of Numerators ) / ( HCF of Denominators ) .

☛ HCM of fractions = ( HCM of Numerators ) / ( LCF of Denominators ) .

___________________

Answer 2

|| ANSWER ||

Firstly Take LCM of 25 , 20 , 24

Now ,

$lcm(25.20.24) = 600$

Now, we want remainder as 7

Therefore

$600 + 7 = 607$

Now , As you can see

$\frac{607}{25} = leaves \: remainder \: 7 \\ \\ \frac{607}{20} = leaves \: remainder \: 7 \\ \\ \frac{607}{24} = leaves \: remainder \: 7$

So , Your least Number is 607.

NOTE :-

• The Least Common Multiple ( LCM ) is also referred to as the Least Common Divisor ( LCD) .
• For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.