LCM of 5 and 7 is the smallest number among all common multiples of 5 and 7. The first few multiples of 5 and 7 are (5, 10, 15, 20, 25, 30, 35, . . . ) and (7, 14, 21, 28, 35, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 7 - by division method, by prime factorization, and by listing multiples.
| 1. | LCM of 5 and 7 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 5 and 7?
Answer: LCM of 5 and 7 is 35.
Explanation:
The LCM of two non-zero integers, x(5) and y(7), is the smallest positive integer m(35) that is divisible by both x(5) and y(7) without any remainder.
Methods to Find LCM of 5 and 7
Let's look at the different methods for finding the LCM of 5 and 7.
- By Division Method
- By Listing Multiples
- By Prime Factorization Method
LCM of 5 and 7 by Division Method
To calculate the LCM of 5 and 7 by the division method, we will divide the numbers(5, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 7.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 7. Write this prime number(5) on the left of the given numbers(5 and 7), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (5, 7) is a multiple of 5, divide it by 5 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 5 and 7 is the product of all prime numbers on the left, i.e. LCM(5, 7) by division method = 5 × 7 = 35.
LCM of 5 and 7 by Listing Multiples
To calculate the LCM of 5 and 7 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, 35, . . . ) and 7 (7, 14, 21, 28, 35, . . . . )
- Step 2: The common multiples from the multiples of 5 and 7 are 35, 70, . . .
- Step 3: The smallest common multiple of 5 and 7 is 35.
∴ The least common multiple of 5 and 7 = 35.
LCM of 5 and 7 by Prime Factorization
Prime factorization of 5 and 7 is (5) = 51 and (7) = 71 respectively. LCM of 5 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 51 × 71 = 35.
Hence, the LCM of 5 and 7 by prime factorization is 35.
☛ Also Check:
- LCM of 9 and 24 - 72
- LCM of 105 and 195 - 1365
- LCM of 10 and 35 - 70
- LCM of 10, 25, 35 and 40 - 1400
- LCM of 63, 70 and 77 - 6930
- LCM of 5, 6 and 7 - 210
- LCM of 14 and 35 - 70
FAQs on LCM of 5 and 7
What is the LCM of 5 and 7?
The LCM of 5 and 7 is 35. To find the LCM (least common multiple) of 5 and 7, we need to find the multiples of 5 and 7 (multiples of 5 = 5, 10, 15, 20 . . . . 35; multiples of 7 = 7, 14, 21, 28 . . . . 35) and choose the smallest multiple that is exactly divisible by 5 and 7, i.e., 35.
If the LCM of 7 and 5 is 35, Find its GCF.
LCM(7, 5) × GCF(7, 5) = 7 × 5
Since the LCM of 7 and 5 = 35
⇒ 35 × GCF(7, 5) = 35
Therefore, the greatest common factor (GCF) = 35/35 = 1.
What are the Methods to Find LCM of 5 and 7?
The commonly used methods to find the LCM of 5 and 7 are:
- Division Method
- Prime Factorization Method
- Listing Multiples
What is the Least Perfect Square Divisible by 5 and 7?
The least number divisible by 5 and 7 = LCM(5, 7)
LCM of 5 and 7 = 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 5 and 7 = LCM(5, 7) × 5 × 7 = 1225 [Square root of 1225 = √1225 = ±35]
Therefore, 1225 is the required number.
How to Find the LCM of 5 and 7 by Prime Factorization?
To find the LCM of 5 and 7 using prime factorization, we will find the prime factors, (5 = 5) and (7 = 7). LCM of 5 and 7 is the product of prime factors raised to their respective highest exponent among the numbers 5 and 7.
⇒ LCM of 5, 7 = 51 × 71 = 35.
