LCM of 40 and 90
LCM of 40 and 90 is the smallest number among all common multiples of 40 and 90. The first few multiples of 40 and 90 are (40, 80, 120, 160, 200, . . . ) and (90, 180, 270, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 40 and 90  by prime factorization, by division method, and by listing multiples.
1.  LCM of 40 and 90 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 40 and 90?
Answer: LCM of 40 and 90 is 360.
Explanation:
The LCM of two nonzero integers, x(40) and y(90), is the smallest positive integer m(360) that is divisible by both x(40) and y(90) without any remainder.
Methods to Find LCM of 40 and 90
Let's look at the different methods for finding the LCM of 40 and 90.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 40 and 90 by Division Method
To calculate the LCM of 40 and 90 by the division method, we will divide the numbers(40, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 40 and 90.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 40 and 90. Write this prime number(2) on the left of the given numbers(40 and 90), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (40, 90) 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 40 and 90 is the product of all prime numbers on the left, i.e. LCM(40, 90) by division method = 2 × 2 × 2 × 3 × 3 × 5 = 360.
LCM of 40 and 90 by Listing Multiples
To calculate the LCM of 40 and 90 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 40 (40, 80, 120, 160, 200, . . . ) and 90 (90, 180, 270, 360, . . . . )
 Step 2: The common multiples from the multiples of 40 and 90 are 360, 720, . . .
 Step 3: The smallest common multiple of 40 and 90 is 360.
∴ The least common multiple of 40 and 90 = 360.
LCM of 40 and 90 by Prime Factorization
Prime factorization of 40 and 90 is (2 × 2 × 2 × 5) = 2^{3} × 5^{1} and (2 × 3 × 3 × 5) = 2^{1} × 3^{2} × 5^{1} respectively. LCM of 40 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{2} × 5^{1} = 360.
Hence, the LCM of 40 and 90 by prime factorization is 360.
☛ Also Check:
 LCM of 36 and 60  180
 LCM of 4 and 7  28
 LCM of 24 and 8  24
 LCM of 12 and 18  36
 LCM of 18 and 40  360
 LCM of 9, 12 and 18  36
 LCM of 10 and 12  60
LCM of 40 and 90 Examples

Example 1: Verify the relationship between GCF and LCM of 40 and 90.
Solution:
The relation between GCF and LCM of 40 and 90 is given as,
LCM(40, 90) × GCF(40, 90) = Product of 40, 90
Prime factorization of 40 and 90 is given as, 40 = (2 × 2 × 2 × 5) = 2^{3} × 5^{1} and 90 = (2 × 3 × 3 × 5) = 2^{1} × 3^{2} × 5^{1}
LCM(40, 90) = 360
GCF(40, 90) = 10
LHS = LCM(40, 90) × GCF(40, 90) = 360 × 10 = 3600
RHS = Product of 40, 90 = 40 × 90 = 3600
⇒ LHS = RHS = 3600
Hence, verified. 
Example 2: Find the smallest number that is divisible by 40 and 90 exactly.
Solution:
The smallest number that is divisible by 40 and 90 exactly is their LCM.
⇒ Multiples of 40 and 90: Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, . . . .
 Multiples of 90 = 90, 180, 270, 360, 450, 540, 630, . . . .
Therefore, the LCM of 40 and 90 is 360.

Example 3: The GCD and LCM of two numbers are 10 and 360 respectively. If one number is 90, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 90 × b
⇒ b = (GCD × LCM)/90
⇒ b = (10 × 360)/90
⇒ b = 40
Therefore, the other number is 40.
FAQs on LCM of 40 and 90
What is the LCM of 40 and 90?
The LCM of 40 and 90 is 360. To find the LCM (least common multiple) of 40 and 90, we need to find the multiples of 40 and 90 (multiples of 40 = 40, 80, 120, 160 . . . . 360; multiples of 90 = 90, 180, 270, 360) and choose the smallest multiple that is exactly divisible by 40 and 90, i.e., 360.
Which of the following is the LCM of 40 and 90? 15, 27, 40, 360
The value of LCM of 40, 90 is the smallest common multiple of 40 and 90. The number satisfying the given condition is 360.
If the LCM of 90 and 40 is 360, Find its GCF.
LCM(90, 40) × GCF(90, 40) = 90 × 40
Since the LCM of 90 and 40 = 360
⇒ 360 × GCF(90, 40) = 3600
Therefore, the GCF (greatest common factor) = 3600/360 = 10.
What are the Methods to Find LCM of 40 and 90?
The commonly used methods to find the LCM of 40 and 90 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
What is the Least Perfect Square Divisible by 40 and 90?
The least number divisible by 40 and 90 = LCM(40, 90)
LCM of 40 and 90 = 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 40 and 90 = LCM(40, 90) × 2 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.
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