What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 51 and 85.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 51 and 85 is 255, where 51 and 85 are less than 255.
  • 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(51, 85) = LCM(85, 51).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 51 and 85 by Listing Method

Example: Find lcm of 51 and 85 by Listing Method

  • Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510, 561, 612, 663, 714, 765, 816, 867, 918, 969, 1020, 1071, 1122, 1173, 1224, 1275, 1326, 1377, 1428, 1479, 1530, 1581, 1632, 1683, 1734, 1785, 1836, 1887, 1938, 1989, 2040, 2091, 2142, 2193, 2244, 2295, 2346, 2397, 2448, 2499, 2550, 2601, 2652, 2703, 2754, 2805, 2856, 2907, 2958, 3009, 3060, 3111, 3162, 3213, 3264, 3315, 3366, 3417, 3468, 3519, 3570, 3621, 3672, 3723, 3774, 3825, 3876, 3927, 3978, 4029, 4080, 4131, 4182, 4233, 4284, 4335
  • Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850, 935, 1020, 1105, 1190, 1275, 1360, 1445, 1530, 1615, 1700, 1785, 1870, 1955, 2040, 2125, 2210, 2295, 2380, 2465, 2550, 2635, 2720, 2805, 2890, 2975, 3060, 3145, 3230, 3315, 3400, 3485, 3570, 3655, 3740, 3825, 3910, 3995, 4080, 4165, 4250, 4335

Hence, LCM of 51 and 85 is 255.

Steps to find LCM of 51 and 85 by Common Division Method

Example: Find lcm of 51 and 85 by Common Division Method

3 51 85
5 17 85
17 17 17
1 1

Hence, LCM of 51 and 85 is 3 x 5 x 17 = 255.

Steps to find lcm of 51 and 85 by Formula

Example: Find lcm of 51 and 85 by Formula

  • GCF of 51 and 85 = 17
  • LCM of 51 and 85 = (51 x 85) / 17
  • => 4335 / 17

Hence, LCM of 51 and 85 is 255.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 51 and 85 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 51 and 85 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 51 and 85.
So, LCM of 51 and 85 is 255.

Both the cricket team and the rugby team had games, today. The cricket team plays every 51 days and the basketball team plays every 85 days. When will both teams have games on the same day again?

Given that the cricket team plays every 51 days and the basketball team plays every 85 days, so for finding the next time when both teams will play again we need to find the LCM of 51 and 85.
So, LCM of 51 and 85 is 255.

Steve spends 51 dollars every day while George spends 85 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 51 and 85.
So, LCM of 51 and 85 is 255.

Boxes that are 51 inches tall are being pilled next to boxes that are 85 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 51 and 85.
So, LCM of 51 and 85 is 255.

Find the LCM of 51 and 85 using GCF method.

Greatest common factor or gcf of 51 and 85 is GCF(51, 85) x LCM(51, 85) = (51 x 85) / GCF(51, 85) = 255.

Find the least common multiple of 51 and 85.

Least common multiple of 51 and 85 is 255.

Find the least number which is exactly divisible by 51 and 85.

Least number which is exactly divisible by 51 and 85 is 255.