Karen Morrison and Nick Hamshaw Solutions for Exercise 9: Exercise 1.9

Use prime factorisation to determine the LCM of following numbers.

$54$ and $90$

Use prime factorisation to determine the LCM of following numbers.

$90$ and $120$

Determine both the HCF and LCM of the following numbers.

$72$ and $108$

Determine both the HCF and LCM of the following numbers.

$25$ and $200$

Determine both the HCF and LCM of the following numbers.

$95$ and $120$

Determine both the HCF and LCM of the following numbers.

$84$ and $60$

A radio station runs a phone-in competition for listeners. Every ${30}^{\mathrm{th}}$ caller gets a free airtime voucher and every ${120}^{\mathrm{th}}$ caller gets a free mobile phone. How many listeners must phone in before one receives both an airtime voucher and a free phone?

Lee runs round a track in $12$ minutes, James runs round the same track in $18$ minutes. If they start in the same place, at the same time, how many minutes will pass before they both cross the start line together again?