LCM of 7 and 15

LCM of 7 and 15 is the smallest number among all common multiples of 7 and 15. The first few multiples of 7 and 15 are (7, 14, 21, 28, . . . ) and (15, 30, 45, 60, 75, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 15 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 7 and 15 is 105.

Explanation:

The LCM of two non-zero integers, x(7) and y(15), is the smallest positive integer m(105) that is divisible by both x(7) and y(15) without any remainder.

The methods to find the LCM of 7 and 15 are explained below.

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

LCM of 7 and 15 by Prime Factorization

Prime factorization of 7 and 15 is (7) = 7¹ and (3 × 5) = 3¹ × 5¹ respectively. LCM of 7 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 7¹ = 105.
Hence, the LCM of 7 and 15 by prime factorization is 105.

LCM of 7 and 15 by Listing Multiples

To calculate the LCM of 7 and 15 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, . . . ) and 15 (15, 30, 45, 60, 75, . . . . )
• Step 2: The common multiples from the multiples of 7 and 15 are 105, 210, . . .
• Step 3: The smallest common multiple of 7 and 15 is 105.

∴ The least common multiple of 7 and 15 = 105.

LCM of 7 and 15 by Division Method

To calculate the LCM of 7 and 15 by the division method, we will divide the numbers(7, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 15. Write this prime number(3) on the left of the given numbers(7 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (7, 15) 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 7 and 15 is the product of all prime numbers on the left, i.e. LCM(7, 15) by division method = 3 × 5 × 7 = 105.

☛ Also Check:

• LCM of 10 and 24 - 120
• LCM of 3, 4 and 9 - 36
• LCM of 24 and 42 - 168
• LCM of 28 and 30 - 420
• LCM of 4 and 5 - 20
• LCM of 5, 10, 15 and 30 - 30
• LCM of 42 and 70 - 210

FAQs on LCM of 7 and 15

What is the LCM of 7 and 15?

The LCM of 7 and 15 is 105. To find the least common multiple (LCM) of 7 and 15, we need to find the multiples of 7 and 15 (multiples of 7 = 7, 14, 21, 28 . . . . 105; multiples of 15 = 15, 30, 45, 60 . . . . 105) and choose the smallest multiple that is exactly divisible by 7 and 15, i.e., 105.

If the LCM of 15 and 7 is 105, Find its GCF.

LCM(15, 7) × GCF(15, 7) = 15 × 7
Since the LCM of 15 and 7 = 105
⇒ 105 × GCF(15, 7) = 105
Therefore, the greatest common factor (GCF) = 105/105 = 1.

What is the Relation Between GCF and LCM of 7, 15?

The following equation can be used to express the relation between GCF and LCM of 7 and 15, i.e. GCF × LCM = 7 × 15.

How to Find the LCM of 7 and 15 by Prime Factorization?

To find the LCM of 7 and 15 using prime factorization, we will find the prime factors, (7 = 7) and (15 = 3 × 5). LCM of 7 and 15 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 15.
⇒ LCM of 7, 15 = 3¹ × 5¹ × 7¹ = 105.

What is the Least Perfect Square Divisible by 7 and 15?

The least number divisible by 7 and 15 = LCM(7, 15)
LCM of 7 and 15 = 3 × 5 × 7 [Incomplete pair(s): 3, 5, 7]
⇒ Least perfect square divisible by each 7 and 15 = LCM(7, 15) × 3 × 5 × 7 = 11025 [Square root of 11025 = √11025 = ±105]
Therefore, 11025 is the required number.