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.
1.  LCM of 90 and 105 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 90 and 105?
Answer: LCM of 90 and 105 is 630.
Explanation:
The LCM of two nonzero 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.
Methods to Find LCM of 90 and 105
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) = 2^{1} × 3^{2} × 5^{1} and (3 × 5 × 7) = 3^{1} × 5^{1} × 7^{1} respectively. LCM of 90 and 105 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 5^{1} × 7^{1} = 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
LCM of 90 and 105 Examples

Example 1: Find the smallest number that is divisible by 90 and 105 exactly.
Solution:
The smallest number that is divisible by 90 and 105 exactly is their LCM.
⇒ Multiples of 90 and 105: Multiples of 90 = 90, 180, 270, 360, 450, 540, 630, . . . .
 Multiples of 105 = 105, 210, 315, 420, 525, 630, . . . .
Therefore, the LCM of 90 and 105 is 630.

Example 2: The product of two numbers is 9450. If their GCD is 15, what is their LCM?
Solution:
Given: GCD = 15
product of numbers = 9450
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 9450/15
Therefore, the LCM is 630.
The probable combination for the given case is LCM(90, 105) = 630. 
Example 3: Verify the relationship between GCF and LCM of 90 and 105.
Solution:
The relation between GCF and LCM of 90 and 105 is given as,
LCM(90, 105) × GCF(90, 105) = Product of 90, 105
Prime factorization of 90 and 105 is given as, 90 = (2 × 3 × 3 × 5) = 2^{1} × 3^{2} × 5^{1} and 105 = (3 × 5 × 7) = 3^{1} × 5^{1} × 7^{1}
LCM(90, 105) = 630
GCF(90, 105) = 15
LHS = LCM(90, 105) × GCF(90, 105) = 630 × 15 = 9450
RHS = Product of 90, 105 = 90 × 105 = 9450
⇒ LHS = RHS = 9450
Hence, verified.
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 = 2^{1} × 3^{2} × 5^{1} × 7^{1} = 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.
visual curriculum