LCM of 520 and 468

LCM of 520 and 468 is the smallest number among all common multiples of 520 and 468. The first few multiples of 520 and 468 are (520, 1040, 1560, 2080, 2600, 3120, . . . ) and (468, 936, 1404, 1872, 2340, . . . ) respectively. There are 3 commonly used methods to find LCM of 520 and 468 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 520 and 468 is 4680.

Explanation:

The LCM of two non-zero integers, x(520) and y(468), is the smallest positive integer m(4680) that is divisible by both x(520) and y(468) without any remainder.

Let's look at the different methods for finding the LCM of 520 and 468.

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

LCM of 520 and 468 by Division Method

To calculate the LCM of 520 and 468 by the division method, we will divide the numbers(520, 468) by their prime factors (preferably common). The product of these divisors gives the LCM of 520 and 468.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 520 and 468. Write this prime number(2) on the left of the given numbers(520 and 468), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (520, 468) is a multiple of 2, divide it by 2 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 520 and 468 is the product of all prime numbers on the left, i.e. LCM(520, 468) by division method = 2 × 2 × 2 × 3 × 3 × 5 × 13 = 4680.

LCM of 520 and 468 by Prime Factorization

Prime factorization of 520 and 468 is (2 × 2 × 2 × 5 × 13) = 2³ × 5¹ × 13¹ and (2 × 2 × 3 × 3 × 13) = 2² × 3² × 13¹ respectively. LCM of 520 and 468 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² × 5¹ × 13¹ = 4680.
Hence, the LCM of 520 and 468 by prime factorization is 4680.

LCM of 520 and 468 by Listing Multiples

To calculate the LCM of 520 and 468 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 520 (520, 1040, 1560, 2080, 2600, 3120, . . . ) and 468 (468, 936, 1404, 1872, 2340, . . . . )
• Step 2: The common multiples from the multiples of 520 and 468 are 4680, 9360, . . .
• Step 3: The smallest common multiple of 520 and 468 is 4680.

∴ The least common multiple of 520 and 468 = 4680.

☛ Also Check:

• LCM of 2, 3 and 5 - 30
• LCM of 15 and 20 - 60
• LCM of 2, 5 and 7 - 70
• LCM of 3, 4 and 7 - 84
• LCM of 16 and 64 - 64
• LCM of 18 and 36 - 36
• LCM of 7 and 17 - 119

FAQs on LCM of 520 and 468

What is the LCM of 520 and 468?

The LCM of 520 and 468 is 4680. To find the least common multiple of 520 and 468, we need to find the multiples of 520 and 468 (multiples of 520 = 520, 1040, 1560, 2080 . . . . 4680; multiples of 468 = 468, 936, 1404, 1872 . . . . 4680) and choose the smallest multiple that is exactly divisible by 520 and 468, i.e., 4680.

What are the Methods to Find LCM of 520 and 468?

The commonly used methods to find the LCM of 520 and 468 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

If the LCM of 468 and 520 is 4680, Find its GCF.

LCM(468, 520) × GCF(468, 520) = 468 × 520
Since the LCM of 468 and 520 = 4680
⇒ 4680 × GCF(468, 520) = 243360
Therefore, the greatest common factor (GCF) = 243360/4680 = 52.

What is the Least Perfect Square Divisible by 520 and 468?

The least number divisible by 520 and 468 = LCM(520, 468)
LCM of 520 and 468 = 2 × 2 × 2 × 3 × 3 × 5 × 13 [Incomplete pair(s): 2, 5, 13]
⇒ Least perfect square divisible by each 520 and 468 = LCM(520, 468) × 2 × 5 × 13 = 608400 [Square root of 608400 = √608400 = ±780]
Therefore, 608400 is the required number.

Which of the following is the LCM of 520 and 468? 15, 20, 4680, 11

The value of LCM of 520, 468 is the smallest common multiple of 520 and 468. The number satisfying the given condition is 4680.