LCM of 4 and 10

LCM of 4 and 10 is the smallest number among all common multiples of 4 and 10. The first few multiples of 4 and 10 are (4, 8, 12, 16, 20, 24, . . . ) and (10, 20, 30, 40, 50, 60, 70, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 10 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 4 and 10 is 20.

Explanation:

The LCM of two non-zero integers, x(4) and y(10), is the smallest positive integer m(20) that is divisible by both x(4) and y(10) without any remainder.

The methods to find the LCM of 4 and 10 are explained below.

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

LCM of 4 and 10 by Prime Factorization

Prime factorization of 4 and 10 is (2 × 2) = 2² and (2 × 5) = 2¹ × 5¹ respectively. LCM of 4 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5¹ = 20.
Hence, the LCM of 4 and 10 by prime factorization is 20.

LCM of 4 and 10 by Listing Multiples

To calculate the LCM of 4 and 10 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, . . . ) and 10 (10, 20, 30, 40, 50, 60, 70, . . . . )
• Step 2: The common multiples from the multiples of 4 and 10 are 20, 40, . . .
• Step 3: The smallest common multiple of 4 and 10 is 20.

∴ The least common multiple of 4 and 10 = 20.

LCM of 4 and 10 by Division Method

To calculate the LCM of 4 and 10 by the division method, we will divide the numbers(4, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 10.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 10. Write this prime number(2) on the left of the given numbers(4 and 10), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 10) 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 4 and 10 is the product of all prime numbers on the left, i.e. LCM(4, 10) by division method = 2 × 2 × 5 = 20.

☛ Also Check:

• LCM of 14 and 21 - 42
• LCM of 2, 4 and 6 - 12
• LCM of 16 and 60 - 240
• LCM of 25 and 36 - 900
• LCM of 14 and 56 - 56
• LCM of 64 and 72 - 576
• LCM of 3, 9 and 18 - 18

FAQs on LCM of 4 and 10

What is the LCM of 4 and 10?

The LCM of 4 and 10 is 20. To find the LCM (least common multiple) of 4 and 10, we need to find the multiples of 4 and 10 (multiples of 4 = 4, 8, 12, 16 . . . . 20; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 4 and 10, i.e., 20.

What are the Methods to Find LCM of 4 and 10?

The commonly used methods to find the LCM of 4 and 10 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

What is the Relation Between GCF and LCM of 4, 10?

The following equation can be used to express the relation between GCF and LCM of 4 and 10, i.e. GCF × LCM = 4 × 10.

If the LCM of 10 and 4 is 20, Find its GCF.

LCM(10, 4) × GCF(10, 4) = 10 × 4
Since the LCM of 10 and 4 = 20
⇒ 20 × GCF(10, 4) = 40
Therefore, the greatest common factor (GCF) = 40/20 = 2.

Which of the following is the LCM of 4 and 10? 28, 20, 32, 2

The value of LCM of 4, 10 is the smallest common multiple of 4 and 10. The number satisfying the given condition is 20.