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LCM of 5 and 35

LCM of 5 and 35 is the smallest number among all common multiples of 5 and 35. The first few multiples of 5 and 35 are (5, 10, 15, 20, 25, . . . ) and (35, 70, 105, 140, 175, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 35 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 5 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 5 and 35?

Answer: LCM of 5 and 35 is 35.

Explanation:

The LCM of two non-zero integers, x(5) and y(35), is the smallest positive integer m(35) that is divisible by both x(5) and y(35) without any remainder.

Methods to Find LCM of 5 and 35

The methods to find the LCM of 5 and 35 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 5 and 35 by Listing Multiples

To calculate the LCM of 5 and 35 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, . . . ) and 35 (35, 70, 105, 140, 175, 210, . . . . )
Step 2: The common multiples from the multiples of 5 and 35 are 35, 70, . . .
Step 3: The smallest common multiple of 5 and 35 is 35.

∴ The least common multiple of 5 and 35 = 35.

LCM of 5 and 35 by Division Method

To calculate the LCM of 5 and 35 by the division method, we will divide the numbers(5, 35) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 35.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 35. Write this prime number(5) on the left of the given numbers(5 and 35), separated as per the ladder arrangement.
Step 2: If any of the given numbers (5, 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 5 and 35 is the product of all prime numbers on the left, i.e. LCM(5, 35) by division method = 5 × 7 = 35.

LCM of 5 and 35 by Prime Factorization

Prime factorization of 5 and 35 is (5) = 5¹ and (5 × 7) = 5¹ × 7¹ respectively. LCM of 5 and 35 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 5¹ × 7¹ = 35.
Hence, the LCM of 5 and 35 by prime factorization is 35.

☛ Also Check:

LCM of 5 and 35 Examples

Example 1: Verify the relationship between GCF and LCM of 5 and 35.

Solution:

The relation between GCF and LCM of 5 and 35 is given as,
LCM(5, 35) × GCF(5, 35) = Product of 5, 35
Prime factorization of 5 and 35 is given as, 5 = (5) = 5¹ and 35 = (5 × 7) = 5¹ × 7¹
LCM(5, 35) = 35
GCF(5, 35) = 5
LHS = LCM(5, 35) × GCF(5, 35) = 35 × 5 = 175
RHS = Product of 5, 35 = 5 × 35 = 175
⇒ LHS = RHS = 175
Hence, verified.
Example 2: The GCD and LCM of two numbers are 5 and 35 respectively. If one number is 5, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 5 × y
⇒ y = (GCD × LCM)/5
⇒ y = (5 × 35)/5
⇒ y = 35
Therefore, the other number is 35.
Example 3: Find the smallest number that is divisible by 5 and 35 exactly.

Solution:

The smallest number that is divisible by 5 and 35 exactly is their LCM.
⇒ Multiples of 5 and 35:
- Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, . . . .
- Multiples of 35 = 35, 70, 105, 140, 175, 210, . . . .
Therefore, the LCM of 5 and 35 is 35.

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FAQs on LCM of 5 and 35

What is the LCM of 5 and 35?

The LCM of 5 and 35 is 35. To find the least common multiple of 5 and 35, we need to find the multiples of 5 and 35 (multiples of 5 = 5, 10, 15, 20 . . . . 35; multiples of 35 = 35, 70, 105, 140) and choose the smallest multiple that is exactly divisible by 5 and 35, i.e., 35.

Which of the following is the LCM of 5 and 35? 35, 11, 18, 36

The value of LCM of 5, 35 is the smallest common multiple of 5 and 35. The number satisfying the given condition is 35.

If the LCM of 35 and 5 is 35, Find its GCF.

LCM(35, 5) × GCF(35, 5) = 35 × 5
Since the LCM of 35 and 5 = 35
⇒ 35 × GCF(35, 5) = 175
Therefore, the greatest common factor = 175/35 = 5.

What is the Relation Between GCF and LCM of 5, 35?

The following equation can be used to express the relation between GCF and LCM of 5 and 35, i.e. GCF × LCM = 5 × 35.

What is the Least Perfect Square Divisible by 5 and 35?

The least number divisible by 5 and 35 = LCM(5, 35)
LCM of 5 and 35 = 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 5 and 35 = LCM(5, 35) × 5 × 7 = 1225 [Square root of 1225 = √1225 = ±35]
Therefore, 1225 is the required number.

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