# Thread: Highest Common Factor and Lowest Common Multiple

1. ## Highest Common Factor and Lowest Common Multiple

1. Find the greatest 4-digit number which is a common multiple of 12,40 and 45.

2. A box contains an assortment of 3 types of chocolate bars.
It has 18 bars with almonds, 24 bars with hazelnuts, and 30 bars with peanuts.
The chocolate bars are shared among some students.
Each student has only 1 type of chocolate bar and every student has the same number of chocolate bars.

Suppose each student has the greatest number of chocolate bars,
(a) how many chocolate bars does each student have? [6]
(b) how many students will have chocolate bars with peanuts? [5]

2. Originally Posted by Drdj
1. Find the greatest 4-digit number which is a common multiple of 12,40 and 45.

2. A box contains an assortment of 3 types of chocolate bars.
It has 18 bars with almonds, 24 bars with hazelnuts, and 30 bars with peanuts.
The chocolate bars are shared among some students.
Each student has only 1 type of chocolate bar and every student has the same number of chocolate bars.

Suppose each student has the greatest number of chocolate bars,
(a) how many chocolate bars does each student have? [6]
(b) how many students will have chocolate bars with peanuts? [5]

$\displaystyle \displaystyle \text{LCM}[12,40]=\frac{12\cdot 40}{\text{GCD}(12,40)}=x$

$\displaystyle \displaystyle\text{LCM}[x,45]=\frac{x\cdot 45}{\text{GCD}(x,45)}$

3. Originally Posted by Drdj
1. Find the greatest 4-digit number which is a common multiple of 12,40 and 45.

2. A box contains an assortment of 3 types of chocolate bars.
It has 18 bars with almonds, 24 bars with hazelnuts, and 30 bars with peanuts.
The chocolate bars are shared among some students.
Each student has only 1 type of chocolate bar and every student has the same number of chocolate bars.

Suppose each student has the greatest number of chocolate bars,
(a) how many chocolate bars does each student have? [6]
(b) how many students will have chocolate bars with peanuts? [5]