## Math 6A, Lesson 3, Fall 2020, 9/27/2020

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1. Least Common Multiple (LCM):

The least common multiple of a group of numbers is the smallest positive integer which is divisible by all the numbers in the group.

The multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …

The multiple of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, …

24 and 48 are the first two common multiples of 6 and 8. Since 24 is the least of all common multiples, we say the least common multiple (LCM) of 6 and 8 is 24.

2. Methods to find LCM

• Using prime factorization. LCM is obtained by multiplying the highest power of each prime factor of the given numbers. Teaching on whiteboard in the class.
• Continuous division. Teaching on whiteboard in the class.
• Venn diagram. Teaching on whiteboard in the class.

3. Why LCM?

• adding, subtracting, or comparing vulgar fractions, it is useful to find the least common multiple of the denominators, often called the lowest common denominator, because each of the fractions can be expressed as a fraction with this denominator. Ex. 1/15 + 1/18 + 1/21
• Word problems: Teaching on whiteboard in the class

4. Home Work:

• Handout: two pages
• Workbook:
• page 2: 7
• Page 3: 13, 15(a), 15(b)(ii), 17(a), 17(b)(ii)
• Page 4: 23
• Page 5: 24