LCM of 35 and 50

LCM of 35 and 50 is the smallest number among all common multiples of 35 and 50. The first few multiples of 35 and 50 are (35, 70, 105, 140, 175, 210, . . . ) and (50, 100, 150, 200, 250, 300, 350, . . . ) respectively. There are 3 commonly used methods to find LCM of 35 and 50 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 35 and 50 is 350.

Explanation:

The LCM of two non-zero integers, x(35) and y(50), is the smallest positive integer m(350) that is divisible by both x(35) and y(50) without any remainder.

Let's look at the different methods for finding the LCM of 35 and 50.

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

LCM of 35 and 50 by Listing Multiples

To calculate the LCM of 35 and 50 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 35 (35, 70, 105, 140, 175, 210, . . . ) and 50 (50, 100, 150, 200, 250, 300, 350, . . . . )
• Step 2: The common multiples from the multiples of 35 and 50 are 350, 700, . . .
• Step 3: The smallest common multiple of 35 and 50 is 350.

∴ The least common multiple of 35 and 50 = 350.

LCM of 35 and 50 by Prime Factorization

Prime factorization of 35 and 50 is (5 × 7) = 5¹ × 7¹ and (2 × 5 × 5) = 2¹ × 5² respectively. LCM of 35 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5² × 7¹ = 350.
Hence, the LCM of 35 and 50 by prime factorization is 350.

LCM of 35 and 50 by Division Method

To calculate the LCM of 35 and 50 by the division method, we will divide the numbers(35, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 35 and 50.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 35 and 50. Write this prime number(2) on the left of the given numbers(35 and 50), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (35, 50) 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 35 and 50 is the product of all prime numbers on the left, i.e. LCM(35, 50) by division method = 2 × 5 × 5 × 7 = 350.

☛ Also Check:

• LCM of 28 and 30 - 420
• LCM of 6 and 14 - 42
• LCM of 3 and 10 - 30
• LCM of 12, 45 and 75 - 900
• LCM of 20, 30 and 60 - 60
• LCM of 54 and 60 - 540
• LCM of 11 and 121 - 121

FAQs on LCM of 35 and 50

What is the LCM of 35 and 50?

The LCM of 35 and 50 is 350. To find the LCM of 35 and 50, we need to find the multiples of 35 and 50 (multiples of 35 = 35, 70, 105, 140 . . . . 350; multiples of 50 = 50, 100, 150, 200 . . . . 350) and choose the smallest multiple that is exactly divisible by 35 and 50, i.e., 350.

How to Find the LCM of 35 and 50 by Prime Factorization?

To find the LCM of 35 and 50 using prime factorization, we will find the prime factors, (35 = 5 × 7) and (50 = 2 × 5 × 5). LCM of 35 and 50 is the product of prime factors raised to their respective highest exponent among the numbers 35 and 50.
⇒ LCM of 35, 50 = 2¹ × 5² × 7¹ = 350.

What is the Relation Between GCF and LCM of 35, 50?

The following equation can be used to express the relation between GCF and LCM of 35 and 50, i.e. GCF × LCM = 35 × 50.

What is the Least Perfect Square Divisible by 35 and 50?

The least number divisible by 35 and 50 = LCM(35, 50)
LCM of 35 and 50 = 2 × 5 × 5 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 35 and 50 = LCM(35, 50) × 2 × 7 = 4900 [Square root of 4900 = √4900 = ±70]
Therefore, 4900 is the required number.

If the LCM of 50 and 35 is 350, Find its GCF.

LCM(50, 35) × GCF(50, 35) = 50 × 35
Since the LCM of 50 and 35 = 350
⇒ 350 × GCF(50, 35) = 1750
Therefore, the GCF (greatest common factor) = 1750/350 = 5.