LCM of 30 and 70

LCM of 30 and 70 is the smallest number among all common multiples of 30 and 70. The first few multiples of 30 and 70 are (30, 60, 90, 120, 150, 180, . . . ) and (70, 140, 210, 280, 350, 420, 490, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 70 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 30 and 70 is 210.

Explanation:

The LCM of two non-zero integers, x(30) and y(70), is the smallest positive integer m(210) that is divisible by both x(30) and y(70) without any remainder.

Let's look at the different methods for finding the LCM of 30 and 70.

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

LCM of 30 and 70 by Listing Multiples

To calculate the LCM of 30 and 70 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 30 (30, 60, 90, 120, 150, 180, . . . ) and 70 (70, 140, 210, 280, 350, 420, 490, . . . . )
• Step 2: The common multiples from the multiples of 30 and 70 are 210, 420, . . .
• Step 3: The smallest common multiple of 30 and 70 is 210.

∴ The least common multiple of 30 and 70 = 210.

LCM of 30 and 70 by Division Method

To calculate the LCM of 30 and 70 by the division method, we will divide the numbers(30, 70) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 70.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 70. Write this prime number(2) on the left of the given numbers(30 and 70), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (30, 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 30 and 70 is the product of all prime numbers on the left, i.e. LCM(30, 70) by division method = 2 × 3 × 5 × 7 = 210.

LCM of 30 and 70 by Prime Factorization

Prime factorization of 30 and 70 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (2 × 5 × 7) = 2¹ × 5¹ × 7¹ respectively. LCM of 30 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 30 and 70 by prime factorization is 210.

☛ Also Check:

• LCM of 10 and 45 - 90
• LCM of 40 and 50 - 200
• LCM of 18, 24 and 30 - 360
• LCM of 54 and 27 - 54
• LCM of 14 and 91 - 182
• LCM of 36, 48 and 54 - 432
• LCM of 15, 30 and 90 - 90

FAQs on LCM of 30 and 70

What is the LCM of 30 and 70?

The LCM of 30 and 70 is 210. To find the least common multiple of 30 and 70, we need to find the multiples of 30 and 70 (multiples of 30 = 30, 60, 90, 120 . . . . 210; multiples of 70 = 70, 140, 210, 280) and choose the smallest multiple that is exactly divisible by 30 and 70, i.e., 210.

What is the Relation Between GCF and LCM of 30, 70?

The following equation can be used to express the relation between GCF and LCM of 30 and 70, i.e. GCF × LCM = 30 × 70.

What are the Methods to Find LCM of 30 and 70?

The commonly used methods to find the LCM of 30 and 70 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 70 and 30 is 210, Find its GCF.

LCM(70, 30) × GCF(70, 30) = 70 × 30
Since the LCM of 70 and 30 = 210
⇒ 210 × GCF(70, 30) = 2100
Therefore, the GCF (greatest common factor) = 2100/210 = 10.

How to Find the LCM of 30 and 70 by Prime Factorization?

To find the LCM of 30 and 70 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (70 = 2 × 5 × 7). LCM of 30 and 70 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 70.
⇒ LCM of 30, 70 = 2¹ × 3¹ × 5¹ × 7¹ = 210.