LCM of 20 and 24 is the smallest number among all common multiples of 20 and 24. The first few multiples of 20 and 24 are (20, 40, 60, 80, . . . ) and (24, 48, 72, 96, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 24 - by prime factorization, by division method, and by listing multiples.
| 1. | LCM of 20 and 24 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 20 and 24?
Answer: LCM of 20 and 24 is 120.
Explanation:
The LCM of two non-zero integers, x(20) and y(24), is the smallest positive integer m(120) that is divisible by both x(20) and y(24) without any remainder.
Methods to Find LCM of 20 and 24
Let's look at the different methods for finding the LCM of 20 and 24.
- By Division Method
- By Listing Multiples
- By Prime Factorization Method
LCM of 20 and 24 by Division Method
To calculate the LCM of 20 and 24 by the division method, we will divide the numbers(20, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 24.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 24. Write this prime number(2) on the left of the given numbers(20 and 24), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (20, 24) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
- Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 20 and 24 is the product of all prime numbers on the left, i.e. LCM(20, 24) by division method = 2 × 2 × 2 × 3 × 5 = 120.
LCM of 20 and 24 by Listing Multiples
To calculate the LCM of 20 and 24 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 20 (20, 40, 60, 80, . . . ) and 24 (24, 48, 72, 96, 120, . . . . )
- Step 2: The common multiples from the multiples of 20 and 24 are 120, 240, . . .
- Step 3: The smallest common multiple of 20 and 24 is 120.
∴ The least common multiple of 20 and 24 = 120.
LCM of 20 and 24 by Prime Factorization
Prime factorization of 20 and 24 is (2 × 2 × 5) = 22 × 51 and (2 × 2 × 2 × 3) = 23 × 31 respectively. LCM of 20 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 51 = 120.
Hence, the LCM of 20 and 24 by prime factorization is 120.
☛ Also Check:
- LCM of 5 and 6 - 30
- LCM of 6 and 27 - 54
- LCM of 21 and 28 - 84
- LCM of 21 and 24 - 168
- LCM of 3, 9 and 21 - 63
- LCM of 2 and 13 - 26
- LCM of 5, 6 and 10 - 30
LCM of 20 and 24 Examples
Example 1: The product of two numbers is 480. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 480
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 480/4
Therefore, the LCM is 120.
The probable combination for the given case is LCM(20, 24) = 120.Example 2: The GCD and LCM of two numbers are 4 and 120 respectively. If one number is 24, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 24 × m
⇒ m = (GCD × LCM)/24
⇒ m = (4 × 120)/24
⇒ m = 20
Therefore, the other number is 20.Example 3: Verify the relationship between GCF and LCM of 20 and 24.
Solution:
The relation between GCF and LCM of 20 and 24 is given as,
LCM(20, 24) × GCF(20, 24) = Product of 20, 24
Prime factorization of 20 and 24 is given as, 20 = (2 × 2 × 5) = 22 × 51 and 24 = (2 × 2 × 2 × 3) = 23 × 31
LCM(20, 24) = 120
GCF(20, 24) = 4
LHS = LCM(20, 24) × GCF(20, 24) = 120 × 4 = 480
RHS = Product of 20, 24 = 20 × 24 = 480
⇒ LHS = RHS = 480
Hence, verified.
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FAQs on LCM of 20 and 24
What is the LCM of 20 and 24?
The LCM of 20 and 24 is 120. To find the least common multiple (LCM) of 20 and 24, we need to find the multiples of 20 and 24 (multiples of 20 = 20, 40, 60, 80 . . . . 120; multiples of 24 = 24, 48, 72, 96 . . . . 120) and choose the smallest multiple that is exactly divisible by 20 and 24, i.e., 120.
If the LCM of 24 and 20 is 120, Find its GCF.
LCM(24, 20) × GCF(24, 20) = 24 × 20
Since the LCM of 24 and 20 = 120
⇒ 120 × GCF(24, 20) = 480
Therefore, the GCF (greatest common factor) = 480/120 = 4.
Which of the following is the LCM of 20 and 24? 120, 30, 42, 40
The value of LCM of 20, 24 is the smallest common multiple of 20 and 24. The number satisfying the given condition is 120.
What is the Relation Between GCF and LCM of 20, 24?
The following equation can be used to express the relation between GCF and LCM of 20 and 24, i.e. GCF × LCM = 20 × 24.
How to Find the LCM of 20 and 24 by Prime Factorization?
To find the LCM of 20 and 24 using prime factorization, we will find the prime factors, (20 = 2 × 2 × 5) and (24 = 2 × 2 × 2 × 3). LCM of 20 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 20 and 24.
⇒ LCM of 20, 24 = 23 × 31 × 51 = 120.
