The smallest number which when diminished by | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the smallest number which when diminished by $7$ is divisible by $12, 16, 18, 21,$ and $28,$ we first need to find the Least Common Multip

Vedclass · Accepted Answer

$1015$

Vedclass · Answer

(B) To find the smallest number which when diminished by $7$ is divisible by $12, 16, 18, 21,$ and $28,$ we first need to find the Least Common Multiple $(LCM)$ of these numbers.Step $1$: Find the prime factorization of each number:$12 = 2^2 	imes 3$$16 = 2^4$$18 = 2 	imes 3^2$$21 = 3 	imes 7$$28 = 2^2 	imes 7$Step $2$: The $LCM$ is the product of the highest powers of all prime factors present:$LCM = 2^4 	imes 3^2 	imes 7 = 16 	imes 9 	imes 7 = 1008$Step $3$: The number which when diminished by $7$ gives $1008$ is $1008 + 7 = 1015$.Therefore,the required number is $1015$.

The smallest number which when diminished by $7,$ is divisible by $12, 16, 18, 21$ and $28$ is

Similar Questions

The product of two numbers is $6760$ and their $H.C.F.$ is $13.$ How many such pairs can be formed?

Find the least number of square tiles required to pave the ceiling of a hall $17 \, m \, 55 \, cm$ long and $8 \, m \, 10 \, cm$ broad.

The $LCM$ of $2^{2} \times 3^{2} \times 5 \times 11$,$2^{4} \times 3^{4} \times 5^{2} \times 7$,and $2^{5} \times 3^{3} \times 5^{2} \times 7^{2} \times 11$ is:

What is the $L.C.M.$ of $25, 30, 35$ and $40$?

The sum of two numbers is $216$ and their $H.C.F.$ is $27$. The numbers are

Vedclass Test Series

Exam Paper Generator

Online Exam Module