We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# GCD stuff

0
131
2

If m and n are positive integers such that gcd(m,n)=12 , then what is the smallest possible value of gcd(10m,15n) ?

Edit: ans=60

Jul 31, 2019
edited by Guest  Jul 31, 2019
edited by Guest  Jul 31, 2019
edited by Guest  Jul 31, 2019

### 2+0 Answers

#1
+1

m = 24

n = 36

GCD =[24, 36] = 12

GCD[24 *10, 36 * 15] =GCD[240, 540] =60

Jul 31, 2019
#2
+23342
+2

If m and n are positive integers such that $$gcd(m,n)=12$$ , then what is the smallest possible value of $$gcd(10m,15n)$$ ?

$$\begin{array}{|rclcrcll|} \hline m&=&12 && n &=& 12 \quad &| \quad \text{m=12 and n=12 are the smallest values for m and n}\\ && && && \quad &| \quad \text{to get gcd(12,12)=12 } \\ &=&2^23 && &=&2^23=12 \quad & | \quad \text{after factorization} \\ && \gcd(12,12) &=& 2^23=12 && \quad & | \quad \text{multiply all prim numbers with the lowest exponent } \\\\ m&=&10*12 && n &=& 15*12 \\ &=&2^33*5 && &=&2^23^25 \quad & | \quad \text{after factorization} \\ && \gcd(120,180) &=& 2^23*5=\mathbf{60} && \quad & | \quad \text{multiply all prim numbers with the lowest exponent } \\ \hline \end{array}$$

Jul 31, 2019