LCM of 15 and 55

LCM of 15 and 55 is the smallest number among all common multiples of 15 and 55. The first few multiples of 15 and 55 are (15, 30, 45, 60, . . . ) and (55, 110, 165, 220, 275, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 55 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 15 and 55 is 165.

Explanation:

The LCM of two non-zero integers, x(15) and y(55), is the smallest positive integer m(165) that is divisible by both x(15) and y(55) without any remainder.

The methods to find the LCM of 15 and 55 are explained below.

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

LCM of 15 and 55 by Prime Factorization

Prime factorization of 15 and 55 is (3 × 5) = 3¹ × 5¹ and (5 × 11) = 5¹ × 11¹ respectively. LCM of 15 and 55 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 11¹ = 165.
Hence, the LCM of 15 and 55 by prime factorization is 165.

LCM of 15 and 55 by Listing Multiples

To calculate the LCM of 15 and 55 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 15 (15, 30, 45, 60, . . . ) and 55 (55, 110, 165, 220, 275, . . . . )
• Step 2: The common multiples from the multiples of 15 and 55 are 165, 330, . . .
• Step 3: The smallest common multiple of 15 and 55 is 165.

∴ The least common multiple of 15 and 55 = 165.

LCM of 15 and 55 by Division Method

To calculate the LCM of 15 and 55 by the division method, we will divide the numbers(15, 55) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 55.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 55. Write this prime number(3) on the left of the given numbers(15 and 55), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (15, 55) is a multiple of 3, divide it by 3 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 15 and 55 is the product of all prime numbers on the left, i.e. LCM(15, 55) by division method = 3 × 5 × 11 = 165.

☛ Also Check:

• LCM of 144 and 169 - 24336
• LCM of 56 and 84 - 168
• LCM of 7 and 17 - 119
• LCM of 28 and 30 - 420
• LCM of 7 and 49 - 49
• LCM of 4, 8 and 12 - 24
• LCM of 4, 9 and 12 - 36

FAQs on LCM of 15 and 55

What is the LCM of 15 and 55?

The LCM of 15 and 55 is 165. To find the LCM (least common multiple) of 15 and 55, we need to find the multiples of 15 and 55 (multiples of 15 = 15, 30, 45, 60 . . . . 165; multiples of 55 = 55, 110, 165, 220) and choose the smallest multiple that is exactly divisible by 15 and 55, i.e., 165.

What is the Relation Between GCF and LCM of 15, 55?

The following equation can be used to express the relation between GCF and LCM of 15 and 55, i.e. GCF × LCM = 15 × 55.

How to Find the LCM of 15 and 55 by Prime Factorization?

To find the LCM of 15 and 55 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (55 = 5 × 11). LCM of 15 and 55 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 55.
⇒ LCM of 15, 55 = 3¹ × 5¹ × 11¹ = 165.

If the LCM of 55 and 15 is 165, Find its GCF.

LCM(55, 15) × GCF(55, 15) = 55 × 15
Since the LCM of 55 and 15 = 165
⇒ 165 × GCF(55, 15) = 825
Therefore, the GCF (greatest common factor) = 825/165 = 5.

Which of the following is the LCM of 15 and 55? 24, 12, 21, 165

The value of LCM of 15, 55 is the smallest common multiple of 15 and 55. The number satisfying the given condition is 165.