CTET Paper II (Mathematics and Science) Nov 2012 Solved Paper

Concept:HCF is the largest number dividing all given numbers. LCM is the smallest number divisible by all given numbers.Explanation:First, write prime factorizations: $4 = 2^2$, $20 = 2^2 \times 5$, $28 = 2^2 \times 7$.HCF takes the lowest power of common primes. Here the common prime is 2 with exponent 2. So HCF = $2^2 = 4$.LCM takes the highest power of all primes appearing. The primes are 2, 5, 7. Highest powers: $2^2$, $5^1$, $7^1$. So LCM = $2^2 \times 5 \times 7 = 4 \times 5 \times 7 = 140$.Now add HCF and LCM: $4 + 140 = 144$.Answer:Option D: 144