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LCM
Two Numbers Three Numbers Multiple Numbers Prime Factorization Division Listing Multiples Ladder Exponents Venn Diagram Factor Tree
HCF
Two Numbers Three Numbers Multiple Numbers Prime Factorization Listing Ladder Exponents Venn Diagram Division Factor Tree All Factors By Division All Factors By Multiplication

LCM Of Two Numbers By Exponents Using Factor Tree

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Answer: LCM of 30, 75 is 150
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Step A: Find the Factors Using Factor Tree

Factor Methods
Factors of 30
30
↙
↘
2
15
↙
↘
3
5
Factors of 75
75
↙
↘
3
25
↙
↘
5
5

Factor Tree Help

1. Always begin with smallest prime.
2. This is the left child of given node.
3. Divide the number by that prime
4. Quotient is the right child of that node.
5. Repeat until right becomes prime factor.
6. Keep tree structure organized.

What is Factor Tree?

The factor tree method is a visual approach used to find the prime factorization of a composite number. It involves breaking down a number into its prime factors by repeatedly dividing it into smaller prime factors until only prime numbers remain which is represent in tree structure.

Step B: Find the LCM Using Exponents

LCM Method
Calculate LCM
30
=
2
1
×
3
1
×
5
1
75
=
3
1
×
5
2

Exponents Help

1. List the Prime Factors with power.
2. Identify Unique Prime Factors.
3. Select factors with high power.
4. Multiply to Find LCM.

What is Exponents?

Exponents method simplifies finding the lowest common multiple or LCM by listing all the prime factors of each number and then selecting the highest power of each common prime factor to obtain the LCM.

Solved Examples

Examples

Example 1: Find the LCM of 12 and 16.
Solution:
Prime factorization of 12: 12 = 2, 2, 3
Prime factorization of 16: 16 = 2, 2, 2, 2
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(12, 16) = 48. Example 2: Find the LCM of 24 and 36.
Solution:
Prime factorization of 24: 24 = 2, 2, 2, 3
Prime factorization of 36: 36 = 2, 2, 3, 3
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(24, 36) = 72. Example 3: Find the LCM of 20 and 80.
Solution:
Prime factorization of 20: 20 = 2, 2, 5
Prime factorization of 80: 80 = 2, 2, 2, 2, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(20, 80) = 80.

Exercise

1. LCM(20,30) = 60. 2. LCM(28,35) = 140. 3. LCM(45,60) = 180. 4. LCM(60,120) = 120. 5. LCM(8,12) = 24. 6. LCM(18,24) = 72. 7. LCM(35,48) = 1680. 8. LCM(72,90) = 360. 9. LCM(10,25) = 50. 10. LCM(6,15) = 30.

Least Common Multiple (LCM)

What is LCM?

LCM or Least Common Multiple, is the smallest number that is divisible by each of the given numbers without leaving a remainder.
The LCM formula can be expressed as,
LCM Formula:
LCM = (a × b)/ HCF(a,b)
where, a and b = Two terms
HCF(a, b) = Highest common factor of a and b.

How to find LCM?

The Least Common Multiple or LCM can be found using various methods, such as: Prime Factorization MethodDivision MethodListing Multiples MethodLadder MethodExponents MethodVenn Diagram Method

FAQ

What are the steps involved to find LCM?
1. Enter two numbers into the calculator.
2. Utilize a factor tree for prime factorization.
3. Convert prime factors into exponent form.
4. Multiply the unique prime factors with highest exponent.
5. Obtain the LCM effortlessly.
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