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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Least common multiple

Grade: 6-a Lesson: S1-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Find the least common multiple 45 and 69.
2	Hint	To find the least common multiple (LCM) of 45 and 69, you can use the prime factorization method.
3	Step	Prime factorization of 45:	\$ 3^2 * 5^1 \$
4	Step	Prime factorization of 69:	\$ 3^1 * 23^1 \$
5	Step	Next, we identify the highest powers of each prime factor, So the highest power of 3 is	\$ 3^2 \$
6	Step	The highest power of 5 is	\$ 5^1 \$
7	Step	The highest power of 23 is	\$ 23^1 \$
8	Step	Multiply the highest powers of each prime factor together	\$ LCM = 3^2 * 5^1 * 23^1 \$
9	Step	After simplification we get	\$ LCM = 9 * 5 * 23 \$
10	Step	After simplification we get	\$ LCM = 1035 \$
11	Sumup	Can you summarize what you’ve understood in the above steps?
12	Choice.A	This statement is incorrect. 1045 divided by 69 equals 15 with a remainder, so it cannot be the least common multiple	1045
13	Choice.B	This is the correct answer because it is the smallest number that is evenly divisible by both 45 and 69	1035
14	Choice.C	This is not divisible by 45 and leaves a remainder of 22. Therefore, it cannot be the least common multiple	1025
15	Choice.D	This is not correct because it does not include all the necessary prime factors	1015
16	Answer	Option	B
17	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Find the least common multiple 45 and 69.

Hint

To find the least common multiple (LCM) of 45 and 69, you can use the prime factorization method.

Step

Prime factorization of 45:

\$ 3^2 * 5^1 \$

Step

Prime factorization of 69:

\$ 3^1 * 23^1 \$

Step

Next, we identify the highest powers of each prime factor, So the highest power of 3 is

\$ 3^2 \$

Step

The highest power of 5 is

\$ 5^1 \$

Step

The highest power of 23 is

\$ 23^1 \$

Step

Multiply the highest powers of each prime factor together

\$ LCM = 3^2 * 5^1 * 23^1 \$

Step

After simplification we get

\$ LCM = 9 * 5 * 23 \$

Step

After simplification we get

\$ LCM = 1035 \$

Sumup

Can you summarize what you’ve understood in the above steps?

Choice.A

This statement is incorrect. 1045 divided by 69 equals 15 with a remainder, so it cannot be the least common multiple

1045

Choice.B

This is the correct answer because it is the smallest number that is evenly divisible by both 45 and 69

1035

Choice.C

This is not divisible by 45 and leaves a remainder of 22. Therefore, it cannot be the least common multiple

1025

Choice.D

This is not correct because it does not include all the necessary prime factors

1015

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?