How do we define LCM?

LCM, abbreviation for least common multiple, is defined as the smallest number that is the product of two or more numbers 37 and 49

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(37, 49) = LCM(49, 37).
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is always greater than the given numbers numbers. Eg- LCM of 37 and 49 is 1813, where 1813 is greater than 37 and 49.

Steps to find lcm of 37 and 49 by Listing Method

Example: Find lcm of 37 and 49 by Listing Method

  • Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370, 407, 444, 481, 518, 555, 592, 629, 666, 703, 740, 777, 814, 851, 888, 925, 962, 999, 1036, 1073, 1110, 1147, 1184, 1221, 1258, 1295, 1332, 1369, 1406, 1443, 1480, 1517, 1554, 1591, 1628, 1665, 1702, 1739, 1776, 1813
  • Multiples of 49: 49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833, 882, 931, 980, 1029, 1078, 1127, 1176, 1225, 1274, 1323, 1372, 1421, 1470, 1519, 1568, 1617, 1666, 1715, 1764, 1813

Hence, LCM of 37 and 49 is 1813.

Steps to find LCM of 37 and 49 by Common Division Method

Example: Find lcm of 37 and 49 by Common Division Method

7 37 49
7 37 7
37 37 1
1 1

Hence, LCM of 37 and 49 is 7 x 7 x 37 = 1813.

Steps to find lcm of 37 and 49 by Formula

Example: Find lcm of 37 and 49 by Formula

  • GCF of 37 and 49 = 1
  • LCM of 37 and 49 = (37 x 49) / 1
  • => 1813 / 1

Hence, LCM of 37 and 49 is 1813.

Examples

Steve spends 37 dollars every day while George spends 49 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 37 and 49.
So, LCM of 37 and 49 is 1813.

Boxes that are 37 inches tall are being pilled next to boxes that are 49 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 37 and 49.
So, LCM of 37 and 49 is 1813.

Sammy's company prints 37 textbooks at a time. Daniel's company prints textbooks in sets of 49 at a time. According to a survey done by a committee, both companies printed the same number of textbooks last year. Find the least number of books that each company would have printed.

To find the least number of textbooks that each company could have printed we need to find the LCM of 37 and 49.
So, LCM of 37 and 49 is 1813.

Ram and Deepika are running on a circular track. They start at the same time. They take 37 and 49 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 37 and 49 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 37 and 49.
So, LCM of 37 and 49 is 1813.

Find the LCM of 37 and 49 using GCF method.

Greatest common factor or gcf of 37 and 49 is GCF(37, 49) x LCM(37, 49) = (37 x 49) / GCF(37, 49) = 1813.

Find the least common multiple of 37 and 49.

Least common multiple of 37 and 49 is 1813.

Find the least number which is exactly divisible by 37 and 49.

Least number which is exactly divisible by 37 and 49 is 1813.