LCM of 37 and 47

LCM of 37 and 47 is the smallest number among all common multiples of 37 and 47. The first few multiples of 37 and 47 are (37, 74, 111, 148, . . . ) and (47, 94, 141, 188, . . . ) respectively. There are 3 commonly used methods to find LCM of 37 and 47 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 37 and 47 is 1739.

Explanation:

The LCM of two non-zero integers, x(37) and y(47), is the smallest positive integer m(1739) that is divisible by both x(37) and y(47) without any remainder.

The methods to find the LCM of 37 and 47 are explained below.

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

LCM of 37 and 47 by Division Method

To calculate the LCM of 37 and 47 by the division method, we will divide the numbers(37, 47) by their prime factors (preferably common). The product of these divisors gives the LCM of 37 and 47.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 37 and 47. Write this prime number(37) on the left of the given numbers(37 and 47), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (37, 47) is a multiple of 37, divide it by 37 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 37 and 47 is the product of all prime numbers on the left, i.e. LCM(37, 47) by division method = 37 × 47 = 1739.

LCM of 37 and 47 by Prime Factorization

Prime factorization of 37 and 47 is (37) = 37¹ and (47) = 47¹ respectively. LCM of 37 and 47 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 37¹ × 47¹ = 1739.
Hence, the LCM of 37 and 47 by prime factorization is 1739.

LCM of 37 and 47 by Listing Multiples

To calculate the LCM of 37 and 47 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 37 (37, 74, 111, 148, . . . ) and 47 (47, 94, 141, 188, . . . . )
• Step 2: The common multiples from the multiples of 37 and 47 are 1739, 3478, . . .
• Step 3: The smallest common multiple of 37 and 47 is 1739.

∴ The least common multiple of 37 and 47 = 1739.

☛ Also Check:

• LCM of 15 and 90 - 90
• LCM of 20 and 22 - 220
• LCM of 80, 85 and 90 - 12240
• LCM of 16, 24 and 40 - 240
• LCM of 3 and 10 - 30
• LCM of 14 and 91 - 182
• LCM of 54 and 72 - 216

FAQs on LCM of 37 and 47

What is the LCM of 37 and 47?

The LCM of 37 and 47 is 1739. To find the LCM of 37 and 47, we need to find the multiples of 37 and 47 (multiples of 37 = 37, 74, 111, 148 . . . . 1739; multiples of 47 = 47, 94, 141, 188 . . . . 1739) and choose the smallest multiple that is exactly divisible by 37 and 47, i.e., 1739.

What is the Relation Between GCF and LCM of 37, 47?

The following equation can be used to express the relation between GCF and LCM of 37 and 47, i.e. GCF × LCM = 37 × 47.

If the LCM of 47 and 37 is 1739, Find its GCF.

LCM(47, 37) × GCF(47, 37) = 47 × 37
Since the LCM of 47 and 37 = 1739
⇒ 1739 × GCF(47, 37) = 1739
Therefore, the GCF = 1739/1739 = 1.

What is the Least Perfect Square Divisible by 37 and 47?

The least number divisible by 37 and 47 = LCM(37, 47)
LCM of 37 and 47 = 37 × 47 [Incomplete pair(s): 37, 47]
⇒ Least perfect square divisible by each 37 and 47 = LCM(37, 47) × 37 × 47 = 3024121 [Square root of 3024121 = √3024121 = ±1739]
Therefore, 3024121 is the required number.

Which of the following is the LCM of 37 and 47? 27, 35, 1739, 20

The value of LCM of 37, 47 is the smallest common multiple of 37 and 47. The number satisfying the given condition is 1739.