LCM of 12 and 35

LCM of 12 and 35 is the smallest number among all common multiples of 12 and 35. The first few multiples of 12 and 35 are (12, 24, 36, 48, 60, 72, . . . ) and (35, 70, 105, 140, 175, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 35 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 12 and 35 is 420.

Explanation:

The LCM of two non-zero integers, x(12) and y(35), is the smallest positive integer m(420) that is divisible by both x(12) and y(35) without any remainder.

The methods to find the LCM of 12 and 35 are explained below.

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

LCM of 12 and 35 by Listing Multiples

To calculate the LCM of 12 and 35 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 35 (35, 70, 105, 140, 175, 210, . . . . )
• Step 2: The common multiples from the multiples of 12 and 35 are 420, 840, . . .
• Step 3: The smallest common multiple of 12 and 35 is 420.

∴ The least common multiple of 12 and 35 = 420.

LCM of 12 and 35 by Prime Factorization

Prime factorization of 12 and 35 is (2 × 2 × 3) = 2² × 3¹ and (5 × 7) = 5¹ × 7¹ respectively. LCM of 12 and 35 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ × 7¹ = 420.
Hence, the LCM of 12 and 35 by prime factorization is 420.

LCM of 12 and 35 by Division Method

To calculate the LCM of 12 and 35 by the division method, we will divide the numbers(12, 35) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 35.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 35. Write this prime number(2) on the left of the given numbers(12 and 35), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 35) 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 12 and 35 is the product of all prime numbers on the left, i.e. LCM(12, 35) by division method = 2 × 2 × 3 × 5 × 7 = 420.

☛ Also Check:

• LCM of 10 and 24 - 120
• LCM of 10 and 20 - 20
• LCM of 10 and 18 - 90
• LCM of 10 and 16 - 80
• LCM of 10 and 15 - 30
• LCM of 10 and 14 - 70
• LCM of 10 and 12 - 60

FAQs on LCM of 12 and 35

What is the LCM of 12 and 35?

The LCM of 12 and 35 is 420. To find the LCM of 12 and 35, we need to find the multiples of 12 and 35 (multiples of 12 = 12, 24, 36, 48 . . . . 420; multiples of 35 = 35, 70, 105, 140 . . . . 420) and choose the smallest multiple that is exactly divisible by 12 and 35, i.e., 420.

What is the Relation Between GCF and LCM of 12, 35?

The following equation can be used to express the relation between GCF and LCM of 12 and 35, i.e. GCF × LCM = 12 × 35.

If the LCM of 35 and 12 is 420, Find its GCF.

LCM(35, 12) × GCF(35, 12) = 35 × 12
Since the LCM of 35 and 12 = 420
⇒ 420 × GCF(35, 12) = 420
Therefore, the greatest common factor = 420/420 = 1.

What is the Least Perfect Square Divisible by 12 and 35?

The least number divisible by 12 and 35 = LCM(12, 35)
LCM of 12 and 35 = 2 × 2 × 3 × 5 × 7 [Incomplete pair(s): 3, 5, 7]
⇒ Least perfect square divisible by each 12 and 35 = LCM(12, 35) × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.

How to Find the LCM of 12 and 35 by Prime Factorization?

To find the LCM of 12 and 35 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (35 = 5 × 7). LCM of 12 and 35 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 35.
⇒ LCM of 12, 35 = 2² × 3¹ × 5¹ × 7¹ = 420.