LCM of 23 and 69

LCM of 23 and 69 is the smallest number among all common multiples of 23 and 69. The first few multiples of 23 and 69 are (23, 46, 69, 92, 115, 138, 161, . . . ) and (69, 138, 207, 276, . . . ) respectively. There are 3 commonly used methods to find LCM of 23 and 69 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 23 and 69 is 69.

Explanation:

The LCM of two non-zero integers, x(23) and y(69), is the smallest positive integer m(69) that is divisible by both x(23) and y(69) without any remainder.

The methods to find the LCM of 23 and 69 are explained below.

• By Division Method
• By Prime Factorization Method
• By Listing Multiples

LCM of 23 and 69 by Division Method

To calculate the LCM of 23 and 69 by the division method, we will divide the numbers(23, 69) by their prime factors (preferably common). The product of these divisors gives the LCM of 23 and 69.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 23 and 69. Write this prime number(3) on the left of the given numbers(23 and 69), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (23, 69) 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 23 and 69 is the product of all prime numbers on the left, i.e. LCM(23, 69) by division method = 3 × 23 = 69.

LCM of 23 and 69 by Prime Factorization

Prime factorization of 23 and 69 is (23) = 23¹ and (3 × 23) = 3¹ × 23¹ respectively. LCM of 23 and 69 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 23¹ = 69.
Hence, the LCM of 23 and 69 by prime factorization is 69.

LCM of 23 and 69 by Listing Multiples

To calculate the LCM of 23 and 69 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 23 (23, 46, 69, 92, 115, 138, 161, . . . ) and 69 (69, 138, 207, 276, . . . . )
• Step 2: The common multiples from the multiples of 23 and 69 are 69, 138, . . .
• Step 3: The smallest common multiple of 23 and 69 is 69.

∴ The least common multiple of 23 and 69 = 69.

☛ Also Check:

• LCM of 2 and 4 - 4
• LCM of 64 and 72 - 576
• LCM of 12, 16, 24 and 36 - 144
• LCM of 8 and 10 - 40
• LCM of 24, 30 and 40 - 120
• LCM of 40 and 50 - 200
• LCM of 60 and 90 - 180

FAQs on LCM of 23 and 69

What is the LCM of 23 and 69?

The LCM of 23 and 69 is 69. To find the least common multiple of 23 and 69, we need to find the multiples of 23 and 69 (multiples of 23 = 23, 46, 69, 92; multiples of 69 = 69, 138, 207, 276) and choose the smallest multiple that is exactly divisible by 23 and 69, i.e., 69.

Which of the following is the LCM of 23 and 69? 30, 36, 69, 27

The value of LCM of 23, 69 is the smallest common multiple of 23 and 69. The number satisfying the given condition is 69.

What is the Relation Between GCF and LCM of 23, 69?

The following equation can be used to express the relation between GCF and LCM of 23 and 69, i.e. GCF × LCM = 23 × 69.

If the LCM of 69 and 23 is 69, Find its GCF.

LCM(69, 23) × GCF(69, 23) = 69 × 23
Since the LCM of 69 and 23 = 69
⇒ 69 × GCF(69, 23) = 1587
Therefore, the GCF (greatest common factor) = 1587/69 = 23.

What are the Methods to Find LCM of 23 and 69?

The commonly used methods to find the LCM of 23 and 69 are:

• Prime Factorization Method
• Division Method
• Listing Multiples