LCM of 45 and 86

LCM of 45 and 86 is the smallest number among all common multiples of 45 and 86. The first few multiples of 45 and 86 are (45, 90, 135, 180, 225, 270, 315, . . . ) and (86, 172, 258, 344, 430, 516, 602, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 86 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 45 and 86 is 3870.

Explanation:

The LCM of two non-zero integers, x(45) and y(86), is the smallest positive integer m(3870) that is divisible by both x(45) and y(86) without any remainder.

Let's look at the different methods for finding the LCM of 45 and 86.

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

LCM of 45 and 86 by Listing Multiples

To calculate the LCM of 45 and 86 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 45 (45, 90, 135, 180, 225, 270, 315, . . . ) and 86 (86, 172, 258, 344, 430, 516, 602, . . . . )
• Step 2: The common multiples from the multiples of 45 and 86 are 3870, 7740, . . .
• Step 3: The smallest common multiple of 45 and 86 is 3870.

∴ The least common multiple of 45 and 86 = 3870.

LCM of 45 and 86 by Prime Factorization

Prime factorization of 45 and 86 is (3 × 3 × 5) = 3² × 5¹ and (2 × 43) = 2¹ × 43¹ respectively. LCM of 45 and 86 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ × 43¹ = 3870.
Hence, the LCM of 45 and 86 by prime factorization is 3870.

LCM of 45 and 86 by Division Method

To calculate the LCM of 45 and 86 by the division method, we will divide the numbers(45, 86) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 86.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 86. Write this prime number(2) on the left of the given numbers(45 and 86), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (45, 86) 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 45 and 86 is the product of all prime numbers on the left, i.e. LCM(45, 86) by division method = 2 × 3 × 3 × 5 × 43 = 3870.

☛ Also Check:

• LCM of 10, 12 and 15 - 60
• LCM of 17 and 8 - 136
• LCM of 20, 25 and 30 - 300
• LCM of 5 and 15 - 15
• LCM of 60 and 66 - 660
• LCM of 6 and 14 - 42
• LCM of 5, 6 and 8 - 120

FAQs on LCM of 45 and 86

What is the LCM of 45 and 86?

The LCM of 45 and 86 is 3870. To find the LCM of 45 and 86, we need to find the multiples of 45 and 86 (multiples of 45 = 45, 90, 135, 180 . . . . 3870; multiples of 86 = 86, 172, 258, 344 . . . . 3870) and choose the smallest multiple that is exactly divisible by 45 and 86, i.e., 3870.

What is the Relation Between GCF and LCM of 45, 86?

The following equation can be used to express the relation between GCF and LCM of 45 and 86, i.e. GCF × LCM = 45 × 86.

Which of the following is the LCM of 45 and 86? 36, 3870, 27, 50

The value of LCM of 45, 86 is the smallest common multiple of 45 and 86. The number satisfying the given condition is 3870.

If the LCM of 86 and 45 is 3870, Find its GCF.

LCM(86, 45) × GCF(86, 45) = 86 × 45
Since the LCM of 86 and 45 = 3870
⇒ 3870 × GCF(86, 45) = 3870
Therefore, the GCF = 3870/3870 = 1.

How to Find the LCM of 45 and 86 by Prime Factorization?

To find the LCM of 45 and 86 using prime factorization, we will find the prime factors, (45 = 3 × 3 × 5) and (86 = 2 × 43). LCM of 45 and 86 is the product of prime factors raised to their respective highest exponent among the numbers 45 and 86.
⇒ LCM of 45, 86 = 2¹ × 3² × 5¹ × 43¹ = 3870.