CTET Paper II (Mathematics and Science) 5 Jan 2022 Solved Paper

Concept:HCF is the greatest number that divides all given numbers exactly. LCM is the smallest number that is a multiple of all given numbers.Explanation:First, find the prime factors of each number:$12 = 2^2 \times 3$$15 = 3 \times 5$$45 = 3^2 \times 5$HCF is the product of the lowest power of common primes. Only 3 is common to all, so HCF = $3$.LCM is the product of the highest power of all primes appearing: $2^2$, $3^2$, and $5$. Thus LCM = $2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180$.Sum = HCF + LCM = $3 + 180 = 183$.Answer:183 (Option A)