LCM of 59 and 29

LCM of 59 and 29 is the smallest number among all common multiples of 59 and 29. The first few multiples of 59 and 29 are (59, 118, 177, 236, . . . ) and (29, 58, 87, 116, 145, 174, 203, . . . ) respectively. There are 3 commonly used methods to find LCM of 59 and 29 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 59 and 29 is 1711.

Explanation:

The LCM of two non-zero integers, x(59) and y(29), is the smallest positive integer m(1711) that is divisible by both x(59) and y(29) without any remainder.

The methods to find the LCM of 59 and 29 are explained below.

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

LCM of 59 and 29 by Listing Multiples

To calculate the LCM of 59 and 29 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 59 (59, 118, 177, 236, . . . ) and 29 (29, 58, 87, 116, 145, 174, 203, . . . . )
• Step 2: The common multiples from the multiples of 59 and 29 are 1711, 3422, . . .
• Step 3: The smallest common multiple of 59 and 29 is 1711.

∴ The least common multiple of 59 and 29 = 1711.

LCM of 59 and 29 by Division Method

To calculate the LCM of 59 and 29 by the division method, we will divide the numbers(59, 29) by their prime factors (preferably common). The product of these divisors gives the LCM of 59 and 29.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 59 and 29. Write this prime number(29) on the left of the given numbers(59 and 29), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (59, 29) is a multiple of 29, divide it by 29 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 59 and 29 is the product of all prime numbers on the left, i.e. LCM(59, 29) by division method = 29 × 59 = 1711.

LCM of 59 and 29 by Prime Factorization

Prime factorization of 59 and 29 is (59) = 59¹ and (29) = 29¹ respectively. LCM of 59 and 29 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 29¹ × 59¹ = 1711.
Hence, the LCM of 59 and 29 by prime factorization is 1711.

☛ Also Check:

• LCM of 64 and 72 - 576
• LCM of 21, 28, 36 and 45 - 1260
• LCM of 10 and 40 - 40
• LCM of 5 and 15 - 15
• LCM of 16 and 18 - 144
• LCM of 15, 25, 40 and 75 - 600
• LCM of 39 and 65 - 195

FAQs on LCM of 59 and 29

What is the LCM of 59 and 29?

The LCM of 59 and 29 is 1711. To find the least common multiple (LCM) of 59 and 29, we need to find the multiples of 59 and 29 (multiples of 59 = 59, 118, 177, 236 . . . . 1711; multiples of 29 = 29, 58, 87, 116 . . . . 1711) and choose the smallest multiple that is exactly divisible by 59 and 29, i.e., 1711.

How to Find the LCM of 59 and 29 by Prime Factorization?

To find the LCM of 59 and 29 using prime factorization, we will find the prime factors, (59 = 59) and (29 = 29). LCM of 59 and 29 is the product of prime factors raised to their respective highest exponent among the numbers 59 and 29.
⇒ LCM of 59, 29 = 29¹ × 59¹ = 1711.

If the LCM of 29 and 59 is 1711, Find its GCF.

LCM(29, 59) × GCF(29, 59) = 29 × 59
Since the LCM of 29 and 59 = 1711
⇒ 1711 × GCF(29, 59) = 1711
Therefore, the GCF = 1711/1711 = 1.

What is the Relation Between GCF and LCM of 59, 29?

The following equation can be used to express the relation between GCF and LCM of 59 and 29, i.e. GCF × LCM = 59 × 29.

Which of the following is the LCM of 59 and 29? 1711, 36, 16, 50

The value of LCM of 59, 29 is the smallest common multiple of 59 and 29. The number satisfying the given condition is 1711.