LCM of 90 and 105

LCM of 90 and 105 is the smallest number among all common multiples of 90 and 105. The first few multiples of 90 and 105 are (90, 180, 270, 360, 450, 540, 630, . . . ) and (105, 210, 315, 420, . . . ) respectively. There are 3 commonly used methods to find LCM of 90 and 105 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 90 and 105 is 630.

Explanation:

The LCM of two non-zero integers, x(90) and y(105), is the smallest positive integer m(630) that is divisible by both x(90) and y(105) without any remainder.

The methods to find the LCM of 90 and 105 are explained below.

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

LCM of 90 and 105 by Listing Multiples

To calculate the LCM of 90 and 105 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 90 (90, 180, 270, 360, 450, 540, 630, . . . ) and 105 (105, 210, 315, 420, . . . . )
• Step 2: The common multiples from the multiples of 90 and 105 are 630, 1260, . . .
• Step 3: The smallest common multiple of 90 and 105 is 630.

∴ The least common multiple of 90 and 105 = 630.

LCM of 90 and 105 by Prime Factorization

Prime factorization of 90 and 105 is (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ and (3 × 5 × 7) = 3¹ × 5¹ × 7¹ respectively. LCM of 90 and 105 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ × 7¹ = 630.
Hence, the LCM of 90 and 105 by prime factorization is 630.

LCM of 90 and 105 by Division Method

To calculate the LCM of 90 and 105 by the division method, we will divide the numbers(90, 105) by their prime factors (preferably common). The product of these divisors gives the LCM of 90 and 105.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 90 and 105. Write this prime number(2) on the left of the given numbers(90 and 105), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (90, 105) 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 90 and 105 is the product of all prime numbers on the left, i.e. LCM(90, 105) by division method = 2 × 3 × 3 × 5 × 7 = 630.

☛ Also Check:

• LCM of 18 and 27 - 54
• LCM of 32 and 80 - 160
• LCM of 9 and 33 - 99
• LCM of 2601 and 2616 - 2268072
• LCM of 11 and 44 - 44
• LCM of 18 and 63 - 126
• LCM of 16 and 28 - 112

FAQs on LCM of 90 and 105

What is the LCM of 90 and 105?

The LCM of 90 and 105 is 630. To find the least common multiple (LCM) of 90 and 105, we need to find the multiples of 90 and 105 (multiples of 90 = 90, 180, 270, 360 . . . . 630; multiples of 105 = 105, 210, 315, 420 . . . . 630) and choose the smallest multiple that is exactly divisible by 90 and 105, i.e., 630.

What are the Methods to Find LCM of 90 and 105?

The commonly used methods to find the LCM of 90 and 105 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

How to Find the LCM of 90 and 105 by Prime Factorization?

To find the LCM of 90 and 105 using prime factorization, we will find the prime factors, (90 = 2 × 3 × 3 × 5) and (105 = 3 × 5 × 7). LCM of 90 and 105 is the product of prime factors raised to their respective highest exponent among the numbers 90 and 105.
⇒ LCM of 90, 105 = 2¹ × 3² × 5¹ × 7¹ = 630.

If the LCM of 105 and 90 is 630, Find its GCF.

LCM(105, 90) × GCF(105, 90) = 105 × 90
Since the LCM of 105 and 90 = 630
⇒ 630 × GCF(105, 90) = 9450
Therefore, the greatest common factor (GCF) = 9450/630 = 15.

What is the Relation Between GCF and LCM of 90, 105?

The following equation can be used to express the relation between GCF and LCM of 90 and 105, i.e. GCF × LCM = 90 × 105.