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LCM of 87 and 145

LCM of 87 and 145 is the smallest number among all common multiples of 87 and 145. The first few multiples of 87 and 145 are (87, 174, 261, 348, . . . ) and (145, 290, 435, 580, . . . ) respectively. There are 3 commonly used methods to find LCM of 87 and 145 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 87 and 145
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 87 and 145?

Answer: LCM of 87 and 145 is 435.

Explanation:

The LCM of two non-zero integers, x(87) and y(145), is the smallest positive integer m(435) that is divisible by both x(87) and y(145) without any remainder.

Methods to Find LCM of 87 and 145

The methods to find the LCM of 87 and 145 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 87 and 145 by Listing Multiples

To calculate the LCM of 87 and 145 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 87 (87, 174, 261, 348, . . . ) and 145 (145, 290, 435, 580, . . . . )
Step 2: The common multiples from the multiples of 87 and 145 are 435, 870, . . .
Step 3: The smallest common multiple of 87 and 145 is 435.

∴ The least common multiple of 87 and 145 = 435.

LCM of 87 and 145 by Prime Factorization

Prime factorization of 87 and 145 is (3 × 29) = 3¹ × 29¹ and (5 × 29) = 5¹ × 29¹ respectively. LCM of 87 and 145 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 29¹ = 435.
Hence, the LCM of 87 and 145 by prime factorization is 435.

LCM of 87 and 145 by Division Method

To calculate the LCM of 87 and 145 by the division method, we will divide the numbers(87, 145) by their prime factors (preferably common). The product of these divisors gives the LCM of 87 and 145.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 87 and 145. Write this prime number(3) on the left of the given numbers(87 and 145), separated as per the ladder arrangement.
Step 2: If any of the given numbers (87, 145) 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 87 and 145 is the product of all prime numbers on the left, i.e. LCM(87, 145) by division method = 3 × 5 × 29 = 435.

☛ Also Check:

LCM of 87 and 145 Examples

Example 1: The GCD and LCM of two numbers are 29 and 435 respectively. If one number is 87, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 87 × b
⇒ b = (GCD × LCM)/87
⇒ b = (29 × 435)/87
⇒ b = 145
Therefore, the other number is 145.
Example 2: Verify the relationship between GCF and LCM of 87 and 145.

Solution:

The relation between GCF and LCM of 87 and 145 is given as,
LCM(87, 145) × GCF(87, 145) = Product of 87, 145
Prime factorization of 87 and 145 is given as, 87 = (3 × 29) = 3¹ × 29¹ and 145 = (5 × 29) = 5¹ × 29¹
LCM(87, 145) = 435
GCF(87, 145) = 29
LHS = LCM(87, 145) × GCF(87, 145) = 435 × 29 = 12615
RHS = Product of 87, 145 = 87 × 145 = 12615
⇒ LHS = RHS = 12615
Hence, verified.
Example 3: The product of two numbers is 12615. If their GCD is 29, what is their LCM?

Solution:

Given: GCD = 29
product of numbers = 12615
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 12615/29
Therefore, the LCM is 435.
The probable combination for the given case is LCM(87, 145) = 435.

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FAQs on LCM of 87 and 145

What is the LCM of 87 and 145?

The LCM of 87 and 145 is 435. To find the LCM of 87 and 145, we need to find the multiples of 87 and 145 (multiples of 87 = 87, 174, 261, 348 . . . . 435; multiples of 145 = 145, 290, 435, 580) and choose the smallest multiple that is exactly divisible by 87 and 145, i.e., 435.

What is the Least Perfect Square Divisible by 87 and 145?

The least number divisible by 87 and 145 = LCM(87, 145)
LCM of 87 and 145 = 3 × 5 × 29 [Incomplete pair(s): 3, 5, 29]
⇒ Least perfect square divisible by each 87 and 145 = LCM(87, 145) × 3 × 5 × 29 = 189225 [Square root of 189225 = √189225 = ±435]
Therefore, 189225 is the required number.

How to Find the LCM of 87 and 145 by Prime Factorization?

To find the LCM of 87 and 145 using prime factorization, we will find the prime factors, (87 = 3 × 29) and (145 = 5 × 29). LCM of 87 and 145 is the product of prime factors raised to their respective highest exponent among the numbers 87 and 145.
⇒ LCM of 87, 145 = 3¹ × 5¹ × 29¹ = 435.

Which of the following is the LCM of 87 and 145? 30, 435, 45, 27

The value of LCM of 87, 145 is the smallest common multiple of 87 and 145. The number satisfying the given condition is 435.

If the LCM of 145 and 87 is 435, Find its GCF.

LCM(145, 87) × GCF(145, 87) = 145 × 87
Since the LCM of 145 and 87 = 435
⇒ 435 × GCF(145, 87) = 12615
Therefore, the GCF (greatest common factor) = 12615/435 = 29.

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