Word Problems on LCM

Q. Rachel opens a biscuit factory. The biscuits of three varieties, A, B, and C, are manufactured.
Each packet has 12, 15, and 21 biscuits, respectively.

For quality check, she has to send packets of each variety such that the number of biscuits are equal.

Find the minimum number of biscuits of each variety sent for quality check.

1. 420
2. 210
3. 840
4. 180

Q.

What is the least positive integer that is divisible by each of $1,3,5$ and $7$?

Q. A shopkeeper sells pens in packet of 12 and markers in packet of 8. What is the least number of pens and markers that Pal should buy so that there will be one pen for each marker.

Q. A shopkeeper sells pens in packet of 12 and markers in packet of 8. What is the least number of pens and markers that Pal should buy so that there will be one pen for each marker.

Q. Cows and Pigeons work together in an animal farm. The cows prepare the fields with their manure and pigeons sow seeds they collect from nearby fields. Cows take a break every $16$ minutes whereas pigeons take a break every $18$ minutes. After how many minutes of starting their day’s work together can they break together?

1. $36$
2. $288$
3. $144$
4. $72$

Q. Class 6A and class 6B students are gathering to select the numbers of best athletes to honor with an award. Class 6A selects athletes in groups of 3 while class 6B selects athletes in groups of 6. If both classes end up with the same number of athletes, what is the smallest number of athletes each must have selected?

Q.

L.C.M. of $10,15$ and $20$ is

1. $30$

2. $60$

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. Emma is packing crates that can hold 5 apples, and Jacob is packing crates that hold 10 apples. If they must pack the same total number of apples, what is the minimum number of apples each must pack?

1. 15
2. 10
3. 5
4. 50