LCM of 4 and 36

LCM of 4 and 36 is the smallest number among all common multiples of 4 and 36. The first few multiples of 4 and 36 are (4, 8, 12, 16, 20, . . . ) and (36, 72, 108, 144, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 36 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 4 and 36 is 36.

Explanation:

The LCM of two non-zero integers, x(4) and y(36), is the smallest positive integer m(36) that is divisible by both x(4) and y(36) without any remainder.

The methods to find the LCM of 4 and 36 are explained below.

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

LCM of 4 and 36 by Division Method

To calculate the LCM of 4 and 36 by the division method, we will divide the numbers(4, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 36.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 36. Write this prime number(2) on the left of the given numbers(4 and 36), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 36) 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 4 and 36 is the product of all prime numbers on the left, i.e. LCM(4, 36) by division method = 2 × 2 × 3 × 3 = 36.

LCM of 4 and 36 by Listing Multiples

To calculate the LCM of 4 and 36 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, . . . ) and 36 (36, 72, 108, 144, 180, . . . . )
• Step 2: The common multiples from the multiples of 4 and 36 are 36, 72, . . .
• Step 3: The smallest common multiple of 4 and 36 is 36.

∴ The least common multiple of 4 and 36 = 36.

LCM of 4 and 36 by Prime Factorization

Prime factorization of 4 and 36 is (2 × 2) = 2² and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 4 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² = 36.
Hence, the LCM of 4 and 36 by prime factorization is 36.

☛ Also Check:

• LCM of 5, 6 and 9 - 90
• LCM of 3, 9 and 12 - 36
• LCM of 8 and 12 - 24
• LCM of 35 and 45 - 315
• LCM of 16 and 30 - 240
• LCM of 5, 8 and 12 - 120
• LCM of 4 and 18 - 36

FAQs on LCM of 4 and 36

What is the LCM of 4 and 36?

The LCM of 4 and 36 is 36. To find the least common multiple of 4 and 36, we need to find the multiples of 4 and 36 (multiples of 4 = 4, 8, 12, 16 . . . . 36; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 4 and 36, i.e., 36.

Which of the following is the LCM of 4 and 36? 3, 18, 36, 28

The value of LCM of 4, 36 is the smallest common multiple of 4 and 36. The number satisfying the given condition is 36.

How to Find the LCM of 4 and 36 by Prime Factorization?

To find the LCM of 4 and 36 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (36 = 2 × 2 × 3 × 3). LCM of 4 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 36.
⇒ LCM of 4, 36 = 2² × 3² = 36.

If the LCM of 36 and 4 is 36, Find its GCF.

LCM(36, 4) × GCF(36, 4) = 36 × 4
Since the LCM of 36 and 4 = 36
⇒ 36 × GCF(36, 4) = 144
Therefore, the GCF = 144/36 = 4.

What is the Least Perfect Square Divisible by 4 and 36?

The least number divisible by 4 and 36 = LCM(4, 36)
LCM of 4 and 36 = 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 4 and 36 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.