What will be the least number which when doubled will be exactly divisible by 24, 18, 21 and 15?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1260
A number divisible by 24, 18, 21 and 15 is a common multiple of all four, and the smallest such number is their LCM. So the doubled number is the LCM, and the number asked for is half the LCM.
Prime factors: \(24=2^{3}\times3\), \(18=2\times3^{2}\), \(21=3\times7\), \(15=3\times5\)
LCM takes the highest power of each prime: \(2^{3}\times3^{2}\times5\times7=2520\)
The number \(=2520\div2=1260\)