LCM of 48 and 72

LCM of 48 and 72 is the smallest number among all common multiples of 48 and 72. The first few multiples of 48 and 72 are (48, 96, 144, 192, . . . ) and (72, 144, 216, 288, 360, 432, 504, . . . ) respectively. There are 3 commonly used methods to find LCM of 48 and 72 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 48 and 72 is 144.

Explanation:

The LCM of two non-zero integers, x(48) and y(72), is the smallest positive integer m(144) that is divisible by both x(48) and y(72) without any remainder.

The methods to find the LCM of 48 and 72 are explained below.

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

LCM of 48 and 72 by Prime Factorization

Prime factorization of 48 and 72 is (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ and (2 × 2 × 2 × 3 × 3) = 2³ × 3² respectively. LCM of 48 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3² = 144.
Hence, the LCM of 48 and 72 by prime factorization is 144.

LCM of 48 and 72 by Division Method

To calculate the LCM of 48 and 72 by the division method, we will divide the numbers(48, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 48 and 72.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 48 and 72. Write this prime number(2) on the left of the given numbers(48 and 72), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (48, 72) 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 48 and 72 is the product of all prime numbers on the left, i.e. LCM(48, 72) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

LCM of 48 and 72 by Listing Multiples

To calculate the LCM of 48 and 72 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 48 (48, 96, 144, 192, . . . ) and 72 (72, 144, 216, 288, 360, 432, 504, . . . . )
• Step 2: The common multiples from the multiples of 48 and 72 are 144, 288, . . .
• Step 3: The smallest common multiple of 48 and 72 is 144.

∴ The least common multiple of 48 and 72 = 144.

☛ Also Check:

• LCM of 4, 7 and 10 - 140
• LCM of 10, 25, 35 and 40 - 1400
• LCM of 8 and 10 - 40
• LCM of 36 and 48 - 144
• LCM of 120 and 160 - 480
• LCM of 100 and 190 - 1900
• LCM of 15 and 18 - 90

FAQs on LCM of 48 and 72

What is the LCM of 48 and 72?

The LCM of 48 and 72 is 144. To find the LCM (least common multiple) of 48 and 72, we need to find the multiples of 48 and 72 (multiples of 48 = 48, 96, 144, 192; multiples of 72 = 72, 144, 216, 288) and choose the smallest multiple that is exactly divisible by 48 and 72, i.e., 144.

Which of the following is the LCM of 48 and 72? 11, 50, 144, 5

The value of LCM of 48, 72 is the smallest common multiple of 48 and 72. The number satisfying the given condition is 144.

What is the Relation Between GCF and LCM of 48, 72?

The following equation can be used to express the relation between GCF and LCM of 48 and 72, i.e. GCF × LCM = 48 × 72.

What are the Methods to Find LCM of 48 and 72?

The commonly used methods to find the LCM of 48 and 72 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 72 and 48 is 144, Find its GCF.

LCM(72, 48) × GCF(72, 48) = 72 × 48
Since the LCM of 72 and 48 = 144
⇒ 144 × GCF(72, 48) = 3456
Therefore, the GCF (greatest common factor) = 3456/144 = 24.