LCM of 5 and 14

LCM of 5 and 14 is the smallest number among all common multiples of 5 and 14. The first few multiples of 5 and 14 are (5, 10, 15, 20, 25, 30, 35, . . . ) and (14, 28, 42, 56, 70, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 14 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 5 and 14 is 70.

Explanation:

The LCM of two non-zero integers, x(5) and y(14), is the smallest positive integer m(70) that is divisible by both x(5) and y(14) without any remainder.

The methods to find the LCM of 5 and 14 are explained below.

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

LCM of 5 and 14 by Prime Factorization

Prime factorization of 5 and 14 is (5) = 5¹ and (2 × 7) = 2¹ × 7¹ respectively. LCM of 5 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5¹ × 7¹ = 70.
Hence, the LCM of 5 and 14 by prime factorization is 70.

LCM of 5 and 14 by Listing Multiples

To calculate the LCM of 5 and 14 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, 35, . . . ) and 14 (14, 28, 42, 56, 70, . . . . )
• Step 2: The common multiples from the multiples of 5 and 14 are 70, 140, . . .
• Step 3: The smallest common multiple of 5 and 14 is 70.

∴ The least common multiple of 5 and 14 = 70.

LCM of 5 and 14 by Division Method

To calculate the LCM of 5 and 14 by the division method, we will divide the numbers(5, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 14.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 14. Write this prime number(2) on the left of the given numbers(5 and 14), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (5, 14) 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 5 and 14 is the product of all prime numbers on the left, i.e. LCM(5, 14) by division method = 2 × 5 × 7 = 70.

☛ Also Check:

• LCM of 7 and 17 - 119
• LCM of 14 and 20 - 140
• LCM of 3, 9 and 12 - 36
• LCM of 21 and 30 - 210
• LCM of 5, 8 and 12 - 120
• LCM of 30 and 60 - 60
• LCM of 9 and 21 - 63

FAQs on LCM of 5 and 14

What is the LCM of 5 and 14?

The LCM of 5 and 14 is 70. To find the LCM (least common multiple) of 5 and 14, we need to find the multiples of 5 and 14 (multiples of 5 = 5, 10, 15, 20 . . . . 70; multiples of 14 = 14, 28, 42, 56 . . . . 70) and choose the smallest multiple that is exactly divisible by 5 and 14, i.e., 70.

Which of the following is the LCM of 5 and 14? 2, 27, 70, 50

The value of LCM of 5, 14 is the smallest common multiple of 5 and 14. The number satisfying the given condition is 70.

What is the Least Perfect Square Divisible by 5 and 14?

The least number divisible by 5 and 14 = LCM(5, 14)
LCM of 5 and 14 = 2 × 5 × 7 [Incomplete pair(s): 2, 5, 7]
⇒ Least perfect square divisible by each 5 and 14 = LCM(5, 14) × 2 × 5 × 7 = 4900 [Square root of 4900 = √4900 = ±70]
Therefore, 4900 is the required number.

If the LCM of 14 and 5 is 70, Find its GCF.

LCM(14, 5) × GCF(14, 5) = 14 × 5
Since the LCM of 14 and 5 = 70
⇒ 70 × GCF(14, 5) = 70
Therefore, the greatest common factor = 70/70 = 1.

What is the Relation Between GCF and LCM of 5, 14?

The following equation can be used to express the relation between GCF and LCM of 5 and 14, i.e. GCF × LCM = 5 × 14.