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LCM of 42 and 70

LCM of 42 and 70 is the smallest number among all common multiples of 42 and 70. The first few multiples of 42 and 70 are (42, 84, 126, 168, 210, 252, 294, . . . ) and (70, 140, 210, 280, 350, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 70 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 42 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 42 and 70?

Answer: LCM of 42 and 70 is 210.

Explanation:

The LCM of two non-zero integers, x(42) and y(70), is the smallest positive integer m(210) that is divisible by both x(42) and y(70) without any remainder.

Methods to Find LCM of 42 and 70

The methods to find the LCM of 42 and 70 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 42 and 70 by Division Method

To calculate the LCM of 42 and 70 by the division method, we will divide the numbers(42, 70) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 70.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 70. Write this prime number(2) on the left of the given numbers(42 and 70), separated as per the ladder arrangement.
Step 2: If any of the given numbers (42, 70) 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 42 and 70 is the product of all prime numbers on the left, i.e. LCM(42, 70) by division method = 2 × 3 × 5 × 7 = 210.

LCM of 42 and 70 by Listing Multiples

To calculate the LCM of 42 and 70 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 42 (42, 84, 126, 168, 210, 252, 294, . . . ) and 70 (70, 140, 210, 280, 350, . . . . )
Step 2: The common multiples from the multiples of 42 and 70 are 210, 420, . . .
Step 3: The smallest common multiple of 42 and 70 is 210.

∴ The least common multiple of 42 and 70 = 210.

LCM of 42 and 70 by Prime Factorization

Prime factorization of 42 and 70 is (2 × 3 × 7) = 2¹ × 3¹ × 7¹ and (2 × 5 × 7) = 2¹ × 5¹ × 7¹ respectively. LCM of 42 and 70 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ × 7¹ = 210.
Hence, the LCM of 42 and 70 by prime factorization is 210.

☛ Also Check:

LCM of 42 and 70 Examples

Example 1: Verify the relationship between GCF and LCM of 42 and 70.

Solution:

The relation between GCF and LCM of 42 and 70 is given as,
LCM(42, 70) × GCF(42, 70) = Product of 42, 70
Prime factorization of 42 and 70 is given as, 42 = (2 × 3 × 7) = 2¹ × 3¹ × 7¹ and 70 = (2 × 5 × 7) = 2¹ × 5¹ × 7¹
LCM(42, 70) = 210
GCF(42, 70) = 14
LHS = LCM(42, 70) × GCF(42, 70) = 210 × 14 = 2940
RHS = Product of 42, 70 = 42 × 70 = 2940
⇒ LHS = RHS = 2940
Hence, verified.
Example 2: The product of two numbers is 2940. If their GCD is 14, what is their LCM?

Solution:

Given: GCD = 14
product of numbers = 2940
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2940/14
Therefore, the LCM is 210.
The probable combination for the given case is LCM(42, 70) = 210.
Example 3: The GCD and LCM of two numbers are 14 and 210 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 = (14 × 210)/70
⇒ z = 42
Therefore, the other number is 42.

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FAQs on LCM of 42 and 70

What is the LCM of 42 and 70?

The LCM of 42 and 70 is 210. To find the LCM (least common multiple) of 42 and 70, we need to find the multiples of 42 and 70 (multiples of 42 = 42, 84, 126, 168 . . . . 210; multiples of 70 = 70, 140, 210, 280) and choose the smallest multiple that is exactly divisible by 42 and 70, i.e., 210.

Which of the following is the LCM of 42 and 70? 18, 210, 45, 20

The value of LCM of 42, 70 is the smallest common multiple of 42 and 70. The number satisfying the given condition is 210.

What is the Relation Between GCF and LCM of 42, 70?

The following equation can be used to express the relation between GCF and LCM of 42 and 70, i.e. GCF × LCM = 42 × 70.

If the LCM of 70 and 42 is 210, Find its GCF.

LCM(70, 42) × GCF(70, 42) = 70 × 42
Since the LCM of 70 and 42 = 210
⇒ 210 × GCF(70, 42) = 2940
Therefore, the greatest common factor (GCF) = 2940/210 = 14.

What is the Least Perfect Square Divisible by 42 and 70?

The least number divisible by 42 and 70 = LCM(42, 70)
LCM of 42 and 70 = 2 × 3 × 5 × 7 [Incomplete pair(s): 2, 3, 5, 7]
⇒ Least perfect square divisible by each 42 and 70 = LCM(42, 70) × 2 × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.

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