LCM of 37 and 49

LCM of 37 and 49 is the smallest number among all common multiples of 37 and 49. The first few multiples of 37 and 49 are (37, 74, 111, 148, . . . ) and (49, 98, 147, 196, 245, 294, . . . ) respectively. There are 3 commonly used methods to find LCM of 37 and 49 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 37 and 49 is 1813.

Explanation:

The LCM of two non-zero integers, x(37) and y(49), is the smallest positive integer m(1813) that is divisible by both x(37) and y(49) without any remainder.

Let's look at the different methods for finding the LCM of 37 and 49.

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

LCM of 37 and 49 by Prime Factorization

Prime factorization of 37 and 49 is (37) = 37¹ and (7 × 7) = 7² respectively. LCM of 37 and 49 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 7² × 37¹ = 1813.
Hence, the LCM of 37 and 49 by prime factorization is 1813.

LCM of 37 and 49 by Listing Multiples

To calculate the LCM of 37 and 49 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 49 (49, 98, 147, 196, 245, 294, . . . . )
• Step 2: The common multiples from the multiples of 37 and 49 are 1813, 3626, . . .
• Step 3: The smallest common multiple of 37 and 49 is 1813.

∴ The least common multiple of 37 and 49 = 1813.

LCM of 37 and 49 by Division Method

To calculate the LCM of 37 and 49 by the division method, we will divide the numbers(37, 49) by their prime factors (preferably common). The product of these divisors gives the LCM of 37 and 49.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 37 and 49. Write this prime number(7) on the left of the given numbers(37 and 49), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (37, 49) is a multiple of 7, divide it by 7 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 49 is the product of all prime numbers on the left, i.e. LCM(37, 49) by division method = 7 × 7 × 37 = 1813.

☛ Also Check:

• LCM of 3, 4 and 7 - 84
• LCM of 8 and 13 - 104
• LCM of 15 and 40 - 120
• LCM of 28 and 32 - 224
• LCM of 36, 60 and 72 - 360
• LCM of 30 and 50 - 150
• LCM of 27 and 36 - 108

FAQs on LCM of 37 and 49

What is the LCM of 37 and 49?

The LCM of 37 and 49 is 1813. To find the least common multiple of 37 and 49, we need to find the multiples of 37 and 49 (multiples of 37 = 37, 74, 111, 148 . . . . 1813; multiples of 49 = 49, 98, 147, 196 . . . . 1813) and choose the smallest multiple that is exactly divisible by 37 and 49, i.e., 1813.

What is the Least Perfect Square Divisible by 37 and 49?

The least number divisible by 37 and 49 = LCM(37, 49)
LCM of 37 and 49 = 7 × 7 × 37 [Incomplete pair(s): 37]
⇒ Least perfect square divisible by each 37 and 49 = LCM(37, 49) × 37 = 67081 [Square root of 67081 = √67081 = ±259]
Therefore, 67081 is the required number.

What is the Relation Between GCF and LCM of 37, 49?

The following equation can be used to express the relation between GCF and LCM of 37 and 49, i.e. GCF × LCM = 37 × 49.

Which of the following is the LCM of 37 and 49? 10, 32, 20, 1813

The value of LCM of 37, 49 is the smallest common multiple of 37 and 49. The number satisfying the given condition is 1813.

If the LCM of 49 and 37 is 1813, Find its GCF.

LCM(49, 37) × GCF(49, 37) = 49 × 37
Since the LCM of 49 and 37 = 1813
⇒ 1813 × GCF(49, 37) = 1813
Therefore, the greatest common factor (GCF) = 1813/1813 = 1.