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LCM of 21 and 35

LCM of 21 and 35 is the smallest number among all common multiples of 21 and 35. The first few multiples of 21 and 35 are (21, 42, 63, 84, 105, 126, 147, . . . ) and (35, 70, 105, 140, 175, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 35 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 21 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 21 and 35?

Answer: LCM of 21 and 35 is 105.

Explanation:

The LCM of two non-zero integers, x(21) and y(35), is the smallest positive integer m(105) that is divisible by both x(21) and y(35) without any remainder.

Methods to Find LCM of 21 and 35

The methods to find the LCM of 21 and 35 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 21 and 35 by Listing Multiples

To calculate the LCM of 21 and 35 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 21 (21, 42, 63, 84, 105, 126, 147, . . . ) and 35 (35, 70, 105, 140, 175, . . . . )
Step 2: The common multiples from the multiples of 21 and 35 are 105, 210, . . .
Step 3: The smallest common multiple of 21 and 35 is 105.

∴ The least common multiple of 21 and 35 = 105.

LCM of 21 and 35 by Prime Factorization

Prime factorization of 21 and 35 is (3 × 7) = 3¹ × 7¹ and (5 × 7) = 5¹ × 7¹ respectively. LCM of 21 and 35 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 7¹ = 105.
Hence, the LCM of 21 and 35 by prime factorization is 105.

LCM of 21 and 35 by Division Method

To calculate the LCM of 21 and 35 by the division method, we will divide the numbers(21, 35) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 35.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 35. Write this prime number(3) on the left of the given numbers(21 and 35), separated as per the ladder arrangement.
Step 2: If any of the given numbers (21, 35) is a multiple of 3, divide it by 3 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 21 and 35 is the product of all prime numbers on the left, i.e. LCM(21, 35) by division method = 3 × 5 × 7 = 105.

☛ Also Check:

LCM of 21 and 35 Examples

Example 1: Verify the relationship between GCF and LCM of 21 and 35.

Solution:

The relation between GCF and LCM of 21 and 35 is given as,
LCM(21, 35) × GCF(21, 35) = Product of 21, 35
Prime factorization of 21 and 35 is given as, 21 = (3 × 7) = 3¹ × 7¹ and 35 = (5 × 7) = 5¹ × 7¹
LCM(21, 35) = 105
GCF(21, 35) = 7
LHS = LCM(21, 35) × GCF(21, 35) = 105 × 7 = 735
RHS = Product of 21, 35 = 21 × 35 = 735
⇒ LHS = RHS = 735
Hence, verified.
Example 2: The product of two numbers is 735. If their GCD is 7, what is their LCM?

Solution:

Given: GCD = 7
product of numbers = 735
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 735/7
Therefore, the LCM is 105.
The probable combination for the given case is LCM(21, 35) = 105.
Example 3: The GCD and LCM of two numbers are 7 and 105 respectively. If one number is 21, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 21 × m
⇒ m = (GCD × LCM)/21
⇒ m = (7 × 105)/21
⇒ m = 35
Therefore, the other number is 35.

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FAQs on LCM of 21 and 35

What is the LCM of 21 and 35?

The LCM of 21 and 35 is 105. To find the LCM of 21 and 35, we need to find the multiples of 21 and 35 (multiples of 21 = 21, 42, 63, 84 . . . . 105; multiples of 35 = 35, 70, 105, 140) and choose the smallest multiple that is exactly divisible by 21 and 35, i.e., 105.

If the LCM of 35 and 21 is 105, Find its GCF.

LCM(35, 21) × GCF(35, 21) = 35 × 21
Since the LCM of 35 and 21 = 105
⇒ 105 × GCF(35, 21) = 735
Therefore, the greatest common factor (GCF) = 735/105 = 7.

How to Find the LCM of 21 and 35 by Prime Factorization?

To find the LCM of 21 and 35 using prime factorization, we will find the prime factors, (21 = 3 × 7) and (35 = 5 × 7). LCM of 21 and 35 is the product of prime factors raised to their respective highest exponent among the numbers 21 and 35.
⇒ LCM of 21, 35 = 3¹ × 5¹ × 7¹ = 105.

Which of the following is the LCM of 21 and 35? 36, 105, 27, 28

The value of LCM of 21, 35 is the smallest common multiple of 21 and 35. The number satisfying the given condition is 105.

What is the Relation Between GCF and LCM of 21, 35?

The following equation can be used to express the relation between GCF and LCM of 21 and 35, i.e. GCF × LCM = 21 × 35.

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