LCM of 120 and 150

LCM of 120 and 150 is the smallest number among all common multiples of 120 and 150. The first few multiples of 120 and 150 are (120, 240, 360, 480, . . . ) and (150, 300, 450, 600, 750, 900, . . . ) respectively. There are 3 commonly used methods to find LCM of 120 and 150 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 120 and 150 is 600.

Explanation:

The LCM of two non-zero integers, x(120) and y(150), is the smallest positive integer m(600) that is divisible by both x(120) and y(150) without any remainder.

The methods to find the LCM of 120 and 150 are explained below.

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

LCM of 120 and 150 by Listing Multiples

To calculate the LCM of 120 and 150 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 120 (120, 240, 360, 480, . . . ) and 150 (150, 300, 450, 600, 750, 900, . . . . )
• Step 2: The common multiples from the multiples of 120 and 150 are 600, 1200, . . .
• Step 3: The smallest common multiple of 120 and 150 is 600.

∴ The least common multiple of 120 and 150 = 600.

LCM of 120 and 150 by Prime Factorization

Prime factorization of 120 and 150 is (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and (2 × 3 × 5 × 5) = 2¹ × 3¹ × 5² respectively. LCM of 120 and 150 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5² = 600.
Hence, the LCM of 120 and 150 by prime factorization is 600.

LCM of 120 and 150 by Division Method

To calculate the LCM of 120 and 150 by the division method, we will divide the numbers(120, 150) by their prime factors (preferably common). The product of these divisors gives the LCM of 120 and 150.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 120 and 150. Write this prime number(2) on the left of the given numbers(120 and 150), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (120, 150) 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 120 and 150 is the product of all prime numbers on the left, i.e. LCM(120, 150) by division method = 2 × 2 × 2 × 3 × 5 × 5 = 600.

☛ Also Check:

• LCM of 4, 9 and 10 - 180
• LCM of 4, 8 and 12 - 24
• LCM of 4, 8 and 10 - 40
• LCM of 4, 8 and 16 - 16
• LCM of 4, 7 and 8 - 56
• LCM of 4, 7 and 14 - 28
• LCM of 4, 6 and 8 - 24

FAQs on LCM of 120 and 150

What is the LCM of 120 and 150?

The LCM of 120 and 150 is 600. To find the least common multiple (LCM) of 120 and 150, we need to find the multiples of 120 and 150 (multiples of 120 = 120, 240, 360, 480 . . . . 600; multiples of 150 = 150, 300, 450, 600) and choose the smallest multiple that is exactly divisible by 120 and 150, i.e., 600.

What is the Relation Between GCF and LCM of 120, 150?

The following equation can be used to express the relation between GCF and LCM of 120 and 150, i.e. GCF × LCM = 120 × 150.

How to Find the LCM of 120 and 150 by Prime Factorization?

To find the LCM of 120 and 150 using prime factorization, we will find the prime factors, (120 = 2 × 2 × 2 × 3 × 5) and (150 = 2 × 3 × 5 × 5). LCM of 120 and 150 is the product of prime factors raised to their respective highest exponent among the numbers 120 and 150.
⇒ LCM of 120, 150 = 2³ × 3¹ × 5² = 600.

Which of the following is the LCM of 120 and 150? 42, 16, 600, 3

The value of LCM of 120, 150 is the smallest common multiple of 120 and 150. The number satisfying the given condition is 600.

If the LCM of 150 and 120 is 600, Find its GCF.

LCM(150, 120) × GCF(150, 120) = 150 × 120
Since the LCM of 150 and 120 = 600
⇒ 600 × GCF(150, 120) = 18000
Therefore, the greatest common factor = 18000/600 = 30.