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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 Division

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

Factor Methods
Factors of 30
2
30
30/2=15
3
15
⤶
15/3=5
5
5
⤶
5/5=1
1
⤶
Factors of 75
3
75
75/3=25
5
25
⤶
25/5=5
5
5
⤶
5/5=1
1
⤶

Division Help

1. Start with the smallest prime.
2. Divide the number by this prime.
3. Write the quotient below.
4. Repeat until the quotient is 1.
5. Confirm using multiplication.

What is Division?

The division method for finding factors begins by dividing the given number by the smallest prime factor like 2, 3,.. This process is repeated with successive primes until the quotient is 1.

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 18 and 36.
Solution:
Prime factorization of 18: 18 = 2, 3, 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(18, 36) = 36. Example 2: Find the LCM of 30 and 40.
Solution:
Prime factorization of 30: 30 = 2, 3, 5
Prime factorization of 40: 40 = 2, 2, 2, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(30, 40) = 120. Example 3: Find the LCM of 112 and 80.
Solution:
Prime factorization of 112: 112 = 2, 2, 2, 2, 7
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(112, 80) = 560.

Exercise

1. LCM(14,21) = 42. 2. LCM(20,30) = 60. 3. LCM(36,48) = 144. 4. LCM(60,75) = 300. 5. LCM(90,100) = 900. 6. LCM(12,80) = 240. 7. LCM(18,24) = 72. 8. LCM(12,15) = 60. 9. LCM(24,36) = 72. 10. LCM(8,10) = 40.

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. Input your numbers into the calculator.
2. Use division method for prime factorization.
3. Convert prime factors into their exponent form.
4. Multiply the unique prime factors with highest exponent.
5. Obtain the LCM.
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