Least Common Multiple (LCM) worksheet for Grade 6 students, focusing on finding the LCM of three numbers.

Here are the step-by-step solutions to find the Least Common Multiple (LCM) for each set of numbers on the worksheet.

1) 14, 21, 7
* Multiples of 21: 21, 42...
* Check 42: It is divisible by 14 ($14 \times 3 = 42$) and by 7 ($7 \times 6 = 42$).
* Answer: 42

2) 13, 29, 21
* These numbers share no common factors other than 1. We multiply them together.
* $13 \times 29 = 377$
* $377 \times 21 = 7917$
* Answer: 7,917

3) 14, 28, 21
* Look at the largest number, 28. Is it divisible by 14? Yes ($14 \times 2$). Is it divisible by 21? No.
* Next multiple of 28 is 56. Divisible by 21? No.
* Next multiple of 28 is 84. Divisible by 21? Yes ($21 \times 4 = 84$).
* Answer: 84

4) 8, 19, 23
* These numbers have no common factors. Multiply them.
* $8 \times 19 = 152$
* $152 \times 23 = 3496$
* Answer: 3,496

5) 19, 14, 8
* Prime factors: $19$ is prime. $14 = 2 \times 7$. $8 = 2^3$.
* LCM must include $19$, $7$, and $2^3$ (which is 8).
* $19 \times 7 \times 8 = 133 \times 8 = 1064$
* Answer: 1,064

6) 18, 29, 21
* Prime factors: $18 = 2 \times 3^2$. $29$ is prime. $21 = 3 \times 7$.
* LCM needs: $2$, $3^2$ (9), $29$, and $7$.
* $2 \times 9 \times 29 \times 7 = 18 \times 203 = 3654$
* Answer: 3,654

7) 24, 11, 14
* Prime factors: $24 = 2^3 \times 3$. $11$ is prime. $14 = 2 \times 7$.
* LCM needs: $2^3$ (8), $3$, $11$, and $7$.
* $8 \times 3 \times 11 \times 7 = 24 \times 77 = 1848$
* Answer: 1,848

8) 17, 30, 11
* These share no common factors. Multiply them.
* $17 \times 30 = 510$
* $510 \times 11 = 5610$
* Answer: 5,610

9) 27, 23, 15
* Prime factors: $27 = 3^3$. $23$ is prime. $15 = 3 \times 5$.
* LCM needs: $3^3$ (27), $23$, and $5$.
* $27 \times 23 \times 5 = 621 \times 5 = 3105$
* Answer: 3,105

10) 21, 11, 15
* Prime factors: $21 = 3 \times 7$. $11$ is prime. $15 = 3 \times 5$.
* LCM needs: $3$, $7$, $11$, and $5$.
* $3 \times 7 \times 11 \times 5 = 21 \times 55 = 1155$
* Answer: 1,155

11) 24, 14, 28
* Notice that 28 is a multiple of 14. So we just need the LCM of 24 and 28.
* Multiples of 28: 28, 56, 84, 112, 140, 168...
* Check 168: $168 \div 24 = 7$. It works.
* Answer: 168

12) 3, 10, 14
* Prime factors: $3$ is prime. $10 = 2 \times 5$. $14 = 2 \times 7$.
* LCM needs: $3$, $2$, $5$, and $7$.
* $3 \times 2 \times 5 \times 7 = 6 \times 35 = 210$
* Answer: 210

13) 9, 13, 26
* Notice that 26 is a multiple of 13 ($13 \times 2$). So we just need the LCM of 9 and 26.
* They share no factors. $9 \times 26 = 234$.
* Answer: 234

14) 9, 27, 2
* Notice that 27 is a multiple of 9. So we just need the LCM of 27 and 2.
* $27 \times 2 = 54$.
* Answer: 54

15) 23, 13, 15
* These share no common factors. Multiply them.
* $23 \times 13 = 299$
* $299 \times 15 = 4485$
* Answer: 4,485

16) 14, 17, 12
* Prime factors: $14 = 2 \times 7$. $17$ is prime. $12 = 2^2 \times 3$.
* LCM needs: $2^2$ (4), $7$, $17$, and $3$.
* $4 \times 7 \times 17 \times 3 = 28 \times 51 = 1428$
* Answer: 1,428

Final Answer:
1) 42
2) 7,917
3) 84
4) 3,496
5) 1,064
6) 3,654
7) 1,848
8) 5,610
9) 3,105
10) 1,155
11) 168
12) 210
13) 234
14) 54
15) 4,485
16) 1,428