Word Problems on LCM

Q. Two bells ring at every 7 minutes and 5 minutes respectively. If two bells ring together at 8:00 AM then the next time they will ring together at

1. 08:35 AM
2. 08:55 AM
3. 08:07 AM
4. 08:05 AM

Q. A radio station runs a phone-in contest for listeners. Every ${40}^{th}$ caller gets a free smartphone and every ${60}^{th}$ caller gets a free laptop. Which caller number is the first to receive both the smartphone and the laptop?

Q. An alarm beeps every $3$ hour, and another alarm beeps every $12$ hour. If they beep at $00:00$ hour, at what time will they again beep together?

1. $06:00$
2. $12:00$

Q. In an orchard, there are two parallel rows of fruit trees, one beside the other. In the first row, every fourth tree is a blackberry tree, and in the second row, every sixth tree is a blueberry tree. The first occurrence of the blackberry tree, where there is a blueberry tree just opposite to it, is .

Q. The high school parade band rehearses with either 7 or 10 members in each line. What is the least number of members that can be present in the marching band ?

1. $35$
2. $70$
3. $105$
4. $50$

Q. Two different machines are used to manufacture a product. The $1^{st}$ machine makes the top part, $14$ in each batch, and the $2^{nd}$ machine makes the bottom part, $16$ in each batch. Each top part is assembled with the bottom part and released to the sales department.

Find the minimum number of batches needs to be produced by the $2^{nd}$ machine such that no unassembled parts are left.

1. $6$
2. $7$
3. $8$
4. $9$

Q. Sebastian and his father went on a driving trip. They want to refuel the car and want to change tyres of the car in minimum time. Gas stations are located at an interval of $40\text{miles}$ and mechanic shops are located at an interval of $30\text{miles}$ from their house in same direction.

Find the minimum distance at which both the gas station and mechanic shop can be located at the same stop.

1. $12\text{miles}$
2. $120\text{miles}$
3. $240\text{miles}$