LCM of 7 and 35 is the smallest number among all common multiples of 7 and 35. The first few multiples of 7 and 35 are (7, 14, 21, 28, 35, 42, . . . ) and (35, 70, 105, 140, 175, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 35 - by prime factorization, by division method, and by listing multiples.
| 1. | LCM of 7 and 35 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 7 and 35?
Answer: LCM of 7 and 35 is 35.
Explanation:
The LCM of two non-zero integers, x(7) and y(35), is the smallest positive integer m(35) that is divisible by both x(7) and y(35) without any remainder.
Methods to Find LCM of 7 and 35
The methods to find the LCM of 7 and 35 are explained below.
- By Listing Multiples
- By Prime Factorization Method
- By Division Method
LCM of 7 and 35 by Listing Multiples
To calculate the LCM of 7 and 35 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, . . . ) and 35 (35, 70, 105, 140, 175, 210, . . . . )
- Step 2: The common multiples from the multiples of 7 and 35 are 35, 70, . . .
- Step 3: The smallest common multiple of 7 and 35 is 35.
∴ The least common multiple of 7 and 35 = 35.
LCM of 7 and 35 by Prime Factorization
Prime factorization of 7 and 35 is (7) = 71 and (5 × 7) = 51 × 71 respectively. LCM of 7 and 35 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 51 × 71 = 35.
Hence, the LCM of 7 and 35 by prime factorization is 35.
LCM of 7 and 35 by Division Method
To calculate the LCM of 7 and 35 by the division method, we will divide the numbers(7, 35) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 35.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 35. Write this prime number(5) on the left of the given numbers(7 and 35), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (7, 35) 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 7 and 35 is the product of all prime numbers on the left, i.e. LCM(7, 35) by division method = 5 × 7 = 35.
☛ Also Check:
- LCM of 45 and 120 - 360
- LCM of 4, 7 and 10 - 140
- LCM of 42 and 56 - 168
- LCM of 7, 8 and 9 - 504
- LCM of 12 and 25 - 300
- LCM of 14 and 42 - 42
- LCM of 200 and 300 - 600
FAQs on LCM of 7 and 35
What is the LCM of 7 and 35?
The LCM of 7 and 35 is 35. To find the LCM of 7 and 35, we need to find the multiples of 7 and 35 (multiples of 7 = 7, 14, 21, 28 . . . . 35; multiples of 35 = 35, 70, 105, 140) and choose the smallest multiple that is exactly divisible by 7 and 35, i.e., 35.
What are the Methods to Find LCM of 7 and 35?
The commonly used methods to find the LCM of 7 and 35 are:
- Listing Multiples
- Division Method
- Prime Factorization Method
What is the Relation Between GCF and LCM of 7, 35?
The following equation can be used to express the relation between GCF and LCM of 7 and 35, i.e. GCF × LCM = 7 × 35.
How to Find the LCM of 7 and 35 by Prime Factorization?
To find the LCM of 7 and 35 using prime factorization, we will find the prime factors, (7 = 7) and (35 = 5 × 7). LCM of 7 and 35 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 35.
⇒ LCM of 7, 35 = 51 × 71 = 35.
If the LCM of 35 and 7 is 35, Find its GCF.
LCM(35, 7) × GCF(35, 7) = 35 × 7
Since the LCM of 35 and 7 = 35
⇒ 35 × GCF(35, 7) = 245
Therefore, the greatest common factor = 245/35 = 7.
