LCM of 75 and 105

LCM of 75 and 105 is the smallest number among all common multiples of 75 and 105. The first few multiples of 75 and 105 are (75, 150, 225, 300, 375, . . . ) and (105, 210, 315, 420, 525, 630, . . . ) respectively. There are 3 commonly used methods to find LCM of 75 and 105 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 75 and 105 is 525.

Explanation:

The LCM of two non-zero integers, x(75) and y(105), is the smallest positive integer m(525) that is divisible by both x(75) and y(105) without any remainder.

Let's look at the different methods for finding the LCM of 75 and 105.

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

LCM of 75 and 105 by Listing Multiples

To calculate the LCM of 75 and 105 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 75 (75, 150, 225, 300, 375, . . . ) and 105 (105, 210, 315, 420, 525, 630, . . . . )
• Step 2: The common multiples from the multiples of 75 and 105 are 525, 1050, . . .
• Step 3: The smallest common multiple of 75 and 105 is 525.

∴ The least common multiple of 75 and 105 = 525.

LCM of 75 and 105 by Division Method

To calculate the LCM of 75 and 105 by the division method, we will divide the numbers(75, 105) by their prime factors (preferably common). The product of these divisors gives the LCM of 75 and 105.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 75 and 105. Write this prime number(3) on the left of the given numbers(75 and 105), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (75, 105) is a multiple of 3, divide it by 3 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 75 and 105 is the product of all prime numbers on the left, i.e. LCM(75, 105) by division method = 3 × 5 × 5 × 7 = 525.

LCM of 75 and 105 by Prime Factorization

Prime factorization of 75 and 105 is (3 × 5 × 5) = 3¹ × 5² and (3 × 5 × 7) = 3¹ × 5¹ × 7¹ respectively. LCM of 75 and 105 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5² × 7¹ = 525.
Hence, the LCM of 75 and 105 by prime factorization is 525.

☛ Also Check:

• LCM of 12 and 32 - 96
• LCM of 8 and 9 - 72
• LCM of 24 and 64 - 192
• LCM of 3 and 13 - 39
• LCM of 72 and 84 - 504
• LCM of 14 and 49 - 98
• LCM of 28 and 35 - 140

FAQs on LCM of 75 and 105

What is the LCM of 75 and 105?

The LCM of 75 and 105 is 525. To find the least common multiple (LCM) of 75 and 105, we need to find the multiples of 75 and 105 (multiples of 75 = 75, 150, 225, 300 . . . . 525; multiples of 105 = 105, 210, 315, 420 . . . . 525) and choose the smallest multiple that is exactly divisible by 75 and 105, i.e., 525.

What is the Relation Between GCF and LCM of 75, 105?

The following equation can be used to express the relation between GCF and LCM of 75 and 105, i.e. GCF × LCM = 75 × 105.

If the LCM of 105 and 75 is 525, Find its GCF.

LCM(105, 75) × GCF(105, 75) = 105 × 75
Since the LCM of 105 and 75 = 525
⇒ 525 × GCF(105, 75) = 7875
Therefore, the GCF (greatest common factor) = 7875/525 = 15.

Which of the following is the LCM of 75 and 105? 32, 35, 2, 525

The value of LCM of 75, 105 is the smallest common multiple of 75 and 105. The number satisfying the given condition is 525.

What are the Methods to Find LCM of 75 and 105?

The commonly used methods to find the LCM of 75 and 105 are:

• Listing Multiples
• Prime Factorization Method
• Division Method