Find the smallest whole number which is exact | vedclass

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

Question

(D) To find the smallest whole number exactly divisible by a set of numbers,we need to calculate the Least Common Multiple $(LCM)$ of those numbers.St

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(D) To find the smallest whole number exactly divisible by a set of numbers,we need to calculate the Least Common Multiple $(LCM)$ of those numbers.Step $1$: Find the prime factorization of each number:$6 = 2 	imes 3$$8 = 2^3$$15 = 3 	imes 5$$18 = 2 	imes 3^2$$24 = 2^3 	imes 3$Step $2$: Identify the highest power of each prime factor present in the factorizations:Prime factors involved are $2, 3,$ and $5$.Highest power of $2 = 2^3 = 8$Highest power of $3 = 3^2 = 9$Highest power of $5 = 5^1 = 5$Step $3$: Multiply these highest powers to find the $LCM$:$LCM = 8 	imes 9 	imes 5 = 72 	imes 5 = 360$.Therefore,the smallest whole number divisible by $6, 8, 15, 18,$ and $24$ is $360$.

Find the smallest whole number which is exactly divisible by $6, 8, 15, 18$ and $24$.

Similar Questions

Find the least number of five digits which when divided by $8, 12, 16$ and $20$ leaves remainders $1, 5, 9$ and $13$ respectively.

$L.C.M.$ and $H.C.F.$ of two numbers $x$ and $y$ are $315$ and $3,$ respectively. If $x+y=36,$ the value of $\frac{1}{x}+\frac{1}{y}$ is

The ratio of two numbers is $3:4$ and their $HCF$ is $4$. Their $LCM$ is

The $H.C.F.$ of two numbers is $12$ and their difference is $12$. The numbers are:

The $LCM$ of two prime numbers $x$ and $y$ $(x > y)$ is $161$. Find the value of $(3y - x)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module