LCM of 36 and 48

LCM of 36 and 48 is the smallest number among all common multiples of 36 and 48. The first few multiples of 36 and 48 are (36, 72, 108, 144, 180, 216, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 48 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 36 and 48 is 144.

Explanation:

The LCM of two non-zero integers, x(36) and y(48), is the smallest positive integer m(144) that is divisible by both x(36) and y(48) without any remainder.

The methods to find the LCM of 36 and 48 are explained below.

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

LCM of 36 and 48 by Division Method

To calculate the LCM of 36 and 48 by the division method, we will divide the numbers(36, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 48.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 48. Write this prime number(2) on the left of the given numbers(36 and 48), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (36, 48) 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 36 and 48 is the product of all prime numbers on the left, i.e. LCM(36, 48) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

LCM of 36 and 48 by Listing Multiples

To calculate the LCM of 36 and 48 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 36 (36, 72, 108, 144, 180, 216, . . . ) and 48 (48, 96, 144, 192, 240, 288, . . . . )
• Step 2: The common multiples from the multiples of 36 and 48 are 144, 288, . . .
• Step 3: The smallest common multiple of 36 and 48 is 144.

∴ The least common multiple of 36 and 48 = 144.

LCM of 36 and 48 by Prime Factorization

Prime factorization of 36 and 48 is (2 × 2 × 3 × 3) = 2² × 3² and (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ respectively. LCM of 36 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3² = 144.
Hence, the LCM of 36 and 48 by prime factorization is 144.

☛ Also Check:

• LCM of 3, 4 and 5 - 60
• LCM of 36, 54 and 72 - 216
• LCM of 14 and 18 - 126
• LCM of 4, 9 and 10 - 180
• LCM of 9 and 21 - 63
• LCM of 10 and 15 - 30
• LCM of 63 and 21 - 63

FAQs on LCM of 36 and 48

What is the LCM of 36 and 48?

The LCM of 36 and 48 is 144. To find the least common multiple of 36 and 48, we need to find the multiples of 36 and 48 (multiples of 36 = 36, 72, 108, 144; multiples of 48 = 48, 96, 144, 192) and choose the smallest multiple that is exactly divisible by 36 and 48, i.e., 144.

If the LCM of 48 and 36 is 144, Find its GCF.

LCM(48, 36) × GCF(48, 36) = 48 × 36
Since the LCM of 48 and 36 = 144
⇒ 144 × GCF(48, 36) = 1728
Therefore, the greatest common factor = 1728/144 = 12.

Which of the following is the LCM of 36 and 48? 10, 144, 21, 16

The value of LCM of 36, 48 is the smallest common multiple of 36 and 48. The number satisfying the given condition is 144.

What is the Relation Between GCF and LCM of 36, 48?

The following equation can be used to express the relation between GCF and LCM of 36 and 48, i.e. GCF × LCM = 36 × 48.

What is the Least Perfect Square Divisible by 36 and 48?

The least number divisible by 36 and 48 = LCM(36, 48)
LCM of 36 and 48 = 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 36 and 48 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.