Dharma, Bhima, Arjun and Karna are very good friends. One day they brought and donated $₹20, ₹30, ₹40 \mathrm{and} ₹50$ to a charity, respectively. Their Math teacher donated an amount (in $₹$) which is equal to the least common multiple of the amounts (in$₹$) donated by Dharma, Bhima, Arjun and Karna. What is the amount donated by the teacher?

A small-scale industry made different kinds of bulbs. The details are as follows:

These bulbs are packed in cartons. Each carton con­tains same number of bulbs and only one variety. Find the minimum number of cartons required to pack these bulbs.

Find the greatest four-digit number which is common multiple of $12, 16, \mathrm{and} 24$.

Ranga and Pranav are good friends from their child-hood. They play a game in which they select a number from $1 \mathrm{to} 1000$. Ranga selects every ${12}^{\mathrm{th}}$ number and Pranav selects every ${27}^{\mathrm{th}}$ number. What are the num­bers selected by the friends in common?