What is LCM?

In mathematics, least common multiple, which is ordinarily reffered to as LCM is characterized as the smallest non-zero number which is divisible by both given numbers 19 and 34.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 19 and 34 is 646, where 19 and 34 are less than 646.
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(19, 34) = LCM(34, 19).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 19 and 34 by Listing Method

Example: Find lcm of 19 and 34 by Listing Method

  • Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399, 418, 437, 456, 475, 494, 513, 532, 551, 570, 589, 608, 627, 646
  • Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612, 646

Hence, LCM of 19 and 34 is 646.

Steps to find LCM of 19 and 34 by Common Division Method

Example: Find lcm of 19 and 34 by Common Division Method

2 19 34
17 19 17
19 19 1
1 1

Hence, LCM of 19 and 34 is 2 x 17 x 19 = 646.

Steps to find lcm of 19 and 34 by Formula

Example: Find lcm of 19 and 34 by Formula

  • GCF of 19 and 34 = 1
  • LCM of 19 and 34 = (19 x 34) / 1
  • => 646 / 1

Hence, LCM of 19 and 34 is 646.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 19 and 34 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 19 and 34 minutes respectively to go round once. We need to find out at what time (minimum) they will run together again. For this we need to find the LCM of 19 and 34.
So, LCM of 19 and 34 is 646.

Both the cricket team and the rugby team had games, today. The cricket team plays every 19 days and the basketball team plays every 34 days. When will both teams have games on the same day again?

Given that the cricket team plays every 19 days and the basketball team plays every 34 days, so for finding the next time when both teams will play again we need to find the LCM of 19 and 34.
So, LCM of 19 and 34 is 646.

Steve spends 19 dollars every day while George spends 34 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 19 and 34.
So, LCM of 19 and 34 is 646.

Boxes that are 19 inches tall are being pilled next to boxes that are 34 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 19 and 34.
So, LCM of 19 and 34 is 646.

Find the LCM of 19 and 34 using GCF method.

Greatest common factor or gcf of 19 and 34 is GCF(19, 34) x LCM(19, 34) = (19 x 34) / GCF(19, 34) = 646.

Find the least common multiple of 19 and 34.

Least common multiple of 19 and 34 is 646.

Find the least number which is exactly divisible by 19 and 34.

Least number which is exactly divisible by 19 and 34 is 646.