The other number is 308. To solve this, recall that for any two numbers aaa and bbb, the relationship is gcd⁡(a,b)×lcm⁡(a,b)=a×b\gcd(a,b)\times \operatorname{lcm}(a,b)=a\times bgcd(a,b)×lcm(a,b)=a×b. Here, gcd⁡=11\gcd =11gcd=11, lcm⁡=7700\operatorname{lcm}=7700lcm=7700, and one number a=275a=275a=275, so b=11×7700275b=\frac{11\times 7700}{275}b=27511×7700​.

First, simplify: 7700÷275=287700\div 275=287700÷275=28 (since 275×28=7700275\times 28=7700275×28=7700). Then, b=11×28=308b=11\times 28=308b=11×28=308.

Verify: Both 275 (11×2511\times 2511×25) and 308 (11×2811\times 2811×28) share gcd⁡=11\gcd =11gcd=11, and lcm⁡(25,28)=700\operatorname{lcm}(25,28)=700lcm(25,28)=700 (as 25 and 28 are coprime), so lcm⁡=11×700=7700\operatorname{lcm}=11\times 700=7700lcm=11×700=7700.

Step-by-Step Breakdown

  1. Write the formula: 11×7700=275×b11\times 7700=275\times b11×7700=275×b.
  2. Compute product: 11×7700=8470011\times 7700=8470011×7700=84700.
  3. Solve: b=84700÷275=308b=84700\div 275=308b=84700÷275=308.

Quick Facts

  • Prime factors : 275=11×52275=11\times 5^2275=11×52, 308=11×22×7308=11\times 2^2\times 7308=11×22×7.
  • Why it works : Numbers are HCF times coprime parts; product of parts gives LCM/HCF ratio.

TL;DR: The other number is 308.