LCM of 84 and 90

LCM of 84 and 90 is the smallest number among all common multiples of 84 and 90. The first few multiples of 84 and 90 are (84, 168, 252, 336, 420, . . . ) and (90, 180, 270, 360, 450, 540, 630, . . . ) respectively. There are 3 commonly used methods to find LCM of 84 and 90 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 84 and 90 is 1260.

Explanation:

The LCM of two non-zero integers, x(84) and y(90), is the smallest positive integer m(1260) that is divisible by both x(84) and y(90) without any remainder.

The methods to find the LCM of 84 and 90 are explained below.

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

LCM of 84 and 90 by Division Method

To calculate the LCM of 84 and 90 by the division method, we will divide the numbers(84, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 84 and 90.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 84 and 90. Write this prime number(2) on the left of the given numbers(84 and 90), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (84, 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 84 and 90 is the product of all prime numbers on the left, i.e. LCM(84, 90) by division method = 2 × 2 × 3 × 3 × 5 × 7 = 1260.

LCM of 84 and 90 by Listing Multiples

To calculate the LCM of 84 and 90 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 84 (84, 168, 252, 336, 420, . . . ) and 90 (90, 180, 270, 360, 450, 540, 630, . . . . )
• Step 2: The common multiples from the multiples of 84 and 90 are 1260, 2520, . . .
• Step 3: The smallest common multiple of 84 and 90 is 1260.

∴ The least common multiple of 84 and 90 = 1260.

LCM of 84 and 90 by Prime Factorization

Prime factorization of 84 and 90 is (2 × 2 × 3 × 7) = 2² × 3¹ × 7¹ and (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ respectively. LCM of 84 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ × 7¹ = 1260.
Hence, the LCM of 84 and 90 by prime factorization is 1260.

☛ Also Check:

• LCM of 18 and 42 - 126
• LCM of 144 and 169 - 24336
• LCM of 17 and 34 - 34
• LCM of 15 and 18 - 90
• LCM of 3, 5 and 11 - 165
• LCM of 6 and 18 - 18
• LCM of 20 and 22 - 220

FAQs on LCM of 84 and 90

What is the LCM of 84 and 90?

The LCM of 84 and 90 is 1260. To find the least common multiple of 84 and 90, we need to find the multiples of 84 and 90 (multiples of 84 = 84, 168, 252, 336 . . . . 1260; multiples of 90 = 90, 180, 270, 360 . . . . 1260) and choose the smallest multiple that is exactly divisible by 84 and 90, i.e., 1260.

What is the Least Perfect Square Divisible by 84 and 90?

The least number divisible by 84 and 90 = LCM(84, 90)
LCM of 84 and 90 = 2 × 2 × 3 × 3 × 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 84 and 90 = LCM(84, 90) × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.

What is the Relation Between GCF and LCM of 84, 90?

The following equation can be used to express the relation between GCF and LCM of 84 and 90, i.e. GCF × LCM = 84 × 90.

Which of the following is the LCM of 84 and 90? 32, 50, 30, 1260

The value of LCM of 84, 90 is the smallest common multiple of 84 and 90. The number satisfying the given condition is 1260.

If the LCM of 90 and 84 is 1260, Find its GCF.

LCM(90, 84) × GCF(90, 84) = 90 × 84
Since the LCM of 90 and 84 = 1260
⇒ 1260 × GCF(90, 84) = 7560
Therefore, the GCF (greatest common factor) = 7560/1260 = 6.