Prime Factorisation Challenge

Find the lowest common multiple of 126, 168 and 756.

Find the highest common factor of 30, 75 and 225

Find the smallest integer, p, such that 126p is a perfect square.

Find the smallest integer, n, such that 90n is a perfect cube.

Find the smallest integer n such that 252n is a multiple of 270.

A rectangle board measures 40 cm by 28 cm. It is divided into small squares of equal size. Find the largest possible length of the side of a square.

Answer: ______ cm

Three traffic lights along a road turn red at regular intervals of 1 min 15 seconds, 1 min 20 seconds and 1 min 30 seconds respectively. If the three traffic lights turn red at the same time at 6:30 am, when will this next happen again?

Answer: __________ a.m.

The lowest common multiple of 6, 63 and x is 756, find the smallest possible value of x.