Find the text{LCM} and text{GCD} of the follo | vedclass

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

Question

(A) The given numbers are $17$,$23$,and $29$.Since $17$,$23$,and $29$ are all prime numbers,their prime factorizations are:$17 = 17^1 	imes 1^1$$23 =

Vedclass · Accepted Answer

$	ext{LCM} = 11339, 	ext{GCD} = 1$

Vedclass · Answer

(A) The given numbers are $17$,$23$,and $29$.Since $17$,$23$,and $29$ are all prime numbers,their prime factorizations are:$17 = 17^1 	imes 1^1$$23 = 23^1 	imes 1^1$$29 = 29^1 	imes 1^1$$	ext{GCD}$ (Greatest Common Divisor) is the product of the smallest power of each common prime factor. Here,the only common factor is $1$.$	ext{GCD}(17, 23, 29) = 1$$	ext{LCM}$ (Least Common Multiple) is the product of the highest power of each prime factor involved in the numbers.$	ext{LCM}(17, 23, 29) = 17 	imes 23 	imes 29$$17 	imes 23 = 391$$391 	imes 29 = 11339$Therefore,$	ext{LCM} = 11339$ and $	ext{GCD} = 1$.

Find the $\text{LCM}$ and $\text{GCD}$ of the following numbers using the fundamental theorem of arithmetic: $17$,$23$,and $29$.

Similar Questions

What is the largest number that divides $626$,$3127$,and $15628$ and leaves remainders $1$,$2$,and $3$ respectively?

Prove that $21^{n}$ cannot end in zero for any natural number $n \in N$.

Find the square root of $24+2 \sqrt{119}$.

The following real number is expressed in decimal form. Determine whether it is rational or not. If rational,express it in the form of $\frac{p}{q}$. $5 . \overline{123456}$

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module