To find the Least Common Multiple (LCM) of two numbers, we look for the smallest number that both original numbers can divide into evenly.
Here is the step-by-step solution for each pair:
1. 14 and 77
* Multiples of 14: 14, 28, 42, 56, 70,
84,
98,
112,
126,
140,
154...
* Multiples of 77: 77,
154...
* The first match is 154.
* LCM =
154
2. 85 and 34
* $85 = 5 \times 17$
* $34 = 2 \times 17$
* LCM = $2 \times 5 \times 17 = 10 \times 17 = 170$
* LCM =
170
3. 91 and 52
* $91 = 7 \times 13$
* $52 = 4 \times 13$
* LCM = $4 \times 7 \times 13 = 28 \times 13 = 364$
* LCM =
364
4. 72 and 9
* Since 72 is a multiple of 9 ($9 \times 8 = 72$), the LCM is just the larger number.
* LCM =
72
5. 16 and 64
* Since 64 is a multiple of 16 ($16 \times 4 = 64$), the LCM is just the larger number.
* LCM =
64
6. 56 and 36
* $56 = 8 \times 7$
* $36 = 4 \times 9$
* Both share a factor of 4.
* LCM = $4 \times (14 \times 9) = 4 \times 126 = 504$
* LCM =
504
7. 10 and 50
* Since 50 is a multiple of 10 ($10 \times 5 = 50$), the LCM is just the larger number.
* LCM =
50
8. 23 and 69
* Since 69 is a multiple of 23 ($23 \times 3 = 69$), the LCM is just the larger number.
* LCM =
69
9. 55 and 11
* Since 55 is a multiple of 11 ($11 \times 5 = 55$), the LCM is just the larger number.
* LCM =
55
10. 87 and 33
* $87 = 3 \times 29$
* $33 = 3 \times 11$
* LCM = $3 \times 29 \times 11 = 87 \times 11 = 957$
* LCM =
957
11. 63 and 27
* $63 = 9 \times 7$
* $27 = 9 \times 3$
* LCM = $9 \times 7 \times 3 = 63 \times 3 = 189$
* LCM =
189
12. 12 and 78
* $12 = 6 \times 2$
* $78 = 6 \times 13$
* LCM = $6 \times 2 \times 13 = 12 \times 13 = 156$
* LCM =
156
Final Answer:
14 and 77:
154
85 and 34:
170
91 and 52:
364
72 and 9:
72
16 and 64:
64
56 and 36:
504
10 and 50:
50
23 and 69:
69
55 and 11:
55
87 and 33:
957
63 and 27:
189
12 and 78:
156
Parent Tip: Review the logic above to help your child master the concept of finding least common multiple worksheet.
