LCM of 35 and 45

LCM of 35 and 45 is the smallest number among all common multiples of 35 and 45. The first few multiples of 35 and 45 are (35, 70, 105, 140, . . . ) and (45, 90, 135, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 35 and 45 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 35 and 45 is 315.

Explanation:

The LCM of two non-zero integers, x(35) and y(45), is the smallest positive integer m(315) that is divisible by both x(35) and y(45) without any remainder.

The methods to find the LCM of 35 and 45 are explained below.

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

LCM of 35 and 45 by Prime Factorization

Prime factorization of 35 and 45 is (5 × 7) = 5¹ × 7¹ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 35 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5¹ × 7¹ = 315.
Hence, the LCM of 35 and 45 by prime factorization is 315.

LCM of 35 and 45 by Division Method

To calculate the LCM of 35 and 45 by the division method, we will divide the numbers(35, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 35 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 35 and 45. Write this prime number(3) on the left of the given numbers(35 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (35, 45) 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 35 and 45 is the product of all prime numbers on the left, i.e. LCM(35, 45) by division method = 3 × 3 × 5 × 7 = 315.

LCM of 35 and 45 by Listing Multiples

To calculate the LCM of 35 and 45 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, . . . ) and 45 (45, 90, 135, 180, . . . . )
• Step 2: The common multiples from the multiples of 35 and 45 are 315, 630, . . .
• Step 3: The smallest common multiple of 35 and 45 is 315.

∴ The least common multiple of 35 and 45 = 315.

☛ Also Check:

• LCM of 12 and 35 - 420
• LCM of 9, 12 and 15 - 180
• LCM of 24 and 26 - 312
• LCM of 45 and 54 - 270
• LCM of 12, 16 and 18 - 144
• LCM of 48, 56 and 72 - 1008
• LCM of 5 and 8 - 40

FAQs on LCM of 35 and 45

What is the LCM of 35 and 45?

The LCM of 35 and 45 is 315. To find the LCM (least common multiple) of 35 and 45, we need to find the multiples of 35 and 45 (multiples of 35 = 35, 70, 105, 140 . . . . 315; multiples of 45 = 45, 90, 135, 180 . . . . 315) and choose the smallest multiple that is exactly divisible by 35 and 45, i.e., 315.

What is the Relation Between GCF and LCM of 35, 45?

The following equation can be used to express the relation between GCF and LCM of 35 and 45, i.e. GCF × LCM = 35 × 45.

What is the Least Perfect Square Divisible by 35 and 45?

The least number divisible by 35 and 45 = LCM(35, 45)
LCM of 35 and 45 = 3 × 3 × 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 35 and 45 = LCM(35, 45) × 5 × 7 = 11025 [Square root of 11025 = √11025 = ±105]
Therefore, 11025 is the required number.

If the LCM of 45 and 35 is 315, Find its GCF.

LCM(45, 35) × GCF(45, 35) = 45 × 35
Since the LCM of 45 and 35 = 315
⇒ 315 × GCF(45, 35) = 1575
Therefore, the greatest common factor = 1575/315 = 5.

What are the Methods to Find LCM of 35 and 45?

The commonly used methods to find the LCM of 35 and 45 are:

• Prime Factorization Method
• Division Method
• Listing Multiples