What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?

To find the least number which when doubled will be exactly divisible by 12, 18, 21 and 30, we need to find the least common multiple (LCM) of these numbers.

Step 1: Prime factorization of each number

• 12 = 2^2 * 3
• 18 = 2 * 3^2
• 21 = 3 * 7
• 30 = 2 * 3 * 5

Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime numbers obtained from the numbers. So, LCM = 2^2 * 3^2 * 5 * 7 = 420

Step 3: Find the least number Since the number we are looking for, when doubled, should be divisible by the LCM, we divide the LCM by 2 to get the least number. So, the least number = 420 / 2 = 210

Therefore, the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 is 210.