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LCM of 70 and 90

LCM of 70 and 90 is the smallest number among all common multiples of 70 and 90. The first few multiples of 70 and 90 are (70, 140, 210, 280, 350, . . . ) and (90, 180, 270, 360, 450, 540, . . . ) respectively. There are 3 commonly used methods to find LCM of 70 and 90 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 70 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 70 and 90?

Answer: LCM of 70 and 90 is 630.

Explanation:

The LCM of two non-zero integers, x(70) and y(90), is the smallest positive integer m(630) that is divisible by both x(70) and y(90) without any remainder.

Methods to Find LCM of 70 and 90

The methods to find the LCM of 70 and 90 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 70 and 90 by Prime Factorization

Prime factorization of 70 and 90 is (2 × 5 × 7) = 2¹ × 5¹ × 7¹ and (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ respectively. LCM of 70 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ × 7¹ = 630.
Hence, the LCM of 70 and 90 by prime factorization is 630.

LCM of 70 and 90 by Listing Multiples

To calculate the LCM of 70 and 90 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 70 (70, 140, 210, 280, 350, . . . ) and 90 (90, 180, 270, 360, 450, 540, . . . . )
Step 2: The common multiples from the multiples of 70 and 90 are 630, 1260, . . .
Step 3: The smallest common multiple of 70 and 90 is 630.

∴ The least common multiple of 70 and 90 = 630.

LCM of 70 and 90 by Division Method

To calculate the LCM of 70 and 90 by the division method, we will divide the numbers(70, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 70 and 90.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 70 and 90. Write this prime number(2) on the left of the given numbers(70 and 90), separated as per the ladder arrangement.
Step 2: If any of the given numbers (70, 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 70 and 90 is the product of all prime numbers on the left, i.e. LCM(70, 90) by division method = 2 × 3 × 3 × 5 × 7 = 630.

☛ Also Check:

LCM of 70 and 90 Examples

Example 1: The GCD and LCM of two numbers are 10 and 630 respectively. If one number is 70, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 70 × z
⇒ z = (GCD × LCM)/70
⇒ z = (10 × 630)/70
⇒ z = 90
Therefore, the other number is 90.
Example 2: The product of two numbers is 6300. If their GCD is 10, what is their LCM?

Solution:

Given: GCD = 10
product of numbers = 6300
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 6300/10
Therefore, the LCM is 630.
The probable combination for the given case is LCM(70, 90) = 630.
Example 3: Verify the relationship between GCF and LCM of 70 and 90.

Solution:

The relation between GCF and LCM of 70 and 90 is given as,
LCM(70, 90) × GCF(70, 90) = Product of 70, 90
Prime factorization of 70 and 90 is given as, 70 = (2 × 5 × 7) = 2¹ × 5¹ × 7¹ and 90 = (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹
LCM(70, 90) = 630
GCF(70, 90) = 10
LHS = LCM(70, 90) × GCF(70, 90) = 630 × 10 = 6300
RHS = Product of 70, 90 = 70 × 90 = 6300
⇒ LHS = RHS = 6300
Hence, verified.

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FAQs on LCM of 70 and 90

What is the LCM of 70 and 90?

The LCM of 70 and 90 is 630. To find the least common multiple of 70 and 90, we need to find the multiples of 70 and 90 (multiples of 70 = 70, 140, 210, 280 . . . . 630; multiples of 90 = 90, 180, 270, 360 . . . . 630) and choose the smallest multiple that is exactly divisible by 70 and 90, i.e., 630.

If the LCM of 90 and 70 is 630, Find its GCF.

LCM(90, 70) × GCF(90, 70) = 90 × 70
Since the LCM of 90 and 70 = 630
⇒ 630 × GCF(90, 70) = 6300
Therefore, the GCF = 6300/630 = 10.

What are the Methods to Find LCM of 70 and 90?

The commonly used methods to find the LCM of 70 and 90 are:

Division Method
Prime Factorization Method
Listing Multiples

How to Find the LCM of 70 and 90 by Prime Factorization?

To find the LCM of 70 and 90 using prime factorization, we will find the prime factors, (70 = 2 × 5 × 7) and (90 = 2 × 3 × 3 × 5). LCM of 70 and 90 is the product of prime factors raised to their respective highest exponent among the numbers 70 and 90.
⇒ LCM of 70, 90 = 2¹ × 3² × 5¹ × 7¹ = 630.

Which of the following is the LCM of 70 and 90? 32, 10, 12, 630

The value of LCM of 70, 90 is the smallest common multiple of 70 and 90. The number satisfying the given condition is 630.

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