LCM of 49 and 63

LCM of 49 and 63 is the smallest number among all common multiples of 49 and 63. The first few multiples of 49 and 63 are (49, 98, 147, 196, 245, . . . ) and (63, 126, 189, 252, 315, 378, 441, . . . ) respectively. There are 3 commonly used methods to find LCM of 49 and 63 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 49 and 63 is 441.

Explanation:

The LCM of two non-zero integers, x(49) and y(63), is the smallest positive integer m(441) that is divisible by both x(49) and y(63) without any remainder.

Let's look at the different methods for finding the LCM of 49 and 63.

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

LCM of 49 and 63 by Division Method

To calculate the LCM of 49 and 63 by the division method, we will divide the numbers(49, 63) by their prime factors (preferably common). The product of these divisors gives the LCM of 49 and 63.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 49 and 63. Write this prime number(3) on the left of the given numbers(49 and 63), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (49, 63) 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 49 and 63 is the product of all prime numbers on the left, i.e. LCM(49, 63) by division method = 3 × 3 × 7 × 7 = 441.

LCM of 49 and 63 by Listing Multiples

To calculate the LCM of 49 and 63 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 49 (49, 98, 147, 196, 245, . . . ) and 63 (63, 126, 189, 252, 315, 378, 441, . . . . )
• Step 2: The common multiples from the multiples of 49 and 63 are 441, 882, . . .
• Step 3: The smallest common multiple of 49 and 63 is 441.

∴ The least common multiple of 49 and 63 = 441.

LCM of 49 and 63 by Prime Factorization

Prime factorization of 49 and 63 is (7 × 7) = 7² and (3 × 3 × 7) = 3² × 7¹ respectively. LCM of 49 and 63 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 7² = 441.
Hence, the LCM of 49 and 63 by prime factorization is 441.

☛ Also Check:

• LCM of 4 and 7 - 28
• LCM of 15, 20 and 30 - 60
• LCM of 3 and 14 - 42
• LCM of 21, 28, 36 and 45 - 1260
• LCM of 4 and 20 - 20
• LCM of 2, 4 and 5 - 20
• LCM of 20 and 36 - 180

FAQs on LCM of 49 and 63

What is the LCM of 49 and 63?

The LCM of 49 and 63 is 441. To find the least common multiple of 49 and 63, we need to find the multiples of 49 and 63 (multiples of 49 = 49, 98, 147, 196 . . . . 441; multiples of 63 = 63, 126, 189, 252 . . . . 441) and choose the smallest multiple that is exactly divisible by 49 and 63, i.e., 441.

Which of the following is the LCM of 49 and 63? 441, 45, 27, 12

The value of LCM of 49, 63 is the smallest common multiple of 49 and 63. The number satisfying the given condition is 441.

What is the Least Perfect Square Divisible by 49 and 63?

The least number divisible by 49 and 63 = LCM(49, 63)
LCM of 49 and 63 = 3 × 3 × 7 × 7 [No incomplete pair]
⇒ Least perfect square divisible by each 49 and 63 = 441 [Square root of 441 = √441 = ±21]
Therefore, 441 is the required number.

How to Find the LCM of 49 and 63 by Prime Factorization?

To find the LCM of 49 and 63 using prime factorization, we will find the prime factors, (49 = 7 × 7) and (63 = 3 × 3 × 7). LCM of 49 and 63 is the product of prime factors raised to their respective highest exponent among the numbers 49 and 63.
⇒ LCM of 49, 63 = 3² × 7² = 441.

If the LCM of 63 and 49 is 441, Find its GCF.

LCM(63, 49) × GCF(63, 49) = 63 × 49
Since the LCM of 63 and 49 = 441
⇒ 441 × GCF(63, 49) = 3087
Therefore, the GCF = 3087/441 = 7.