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 21 and 42.

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(21, 42) = LCM(42, 21).
  • 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 21 and 42 is 42, where 42 is greater than 21 and 42.

Steps to find lcm of 21 and 42 by Listing Method

Example: Find lcm of 21 and 42 by Listing Method

  • Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882
  • Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630, 672, 714, 756, 798, 840, 882

Hence, LCM of 21 and 42 is 42.

Steps to find LCM of 21 and 42 by Common Division Method

Example: Find lcm of 21 and 42 by Common Division Method

2 21 42
3 21 21
7 7 7
1 1

Hence, LCM of 21 and 42 is 2 x 3 x 7 = 42.

Steps to find lcm of 21 and 42 by Formula

Example: Find lcm of 21 and 42 by Formula

  • GCF of 21 and 42 = 21
  • LCM of 21 and 42 = (21 x 42) / 21
  • => 882 / 21

Hence, LCM of 21 and 42 is 42.

Examples

Steve spends 21 dollars every day while George spends 42 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 21 and 42.
So, LCM of 21 and 42 is 42.

Boxes that are 21 inches tall are being pilled next to boxes that are 42 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 21 and 42.
So, LCM of 21 and 42 is 42.

Sammy's company prints 21 textbooks at a time. Daniel's company prints textbooks in sets of 42 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 21 and 42.
So, LCM of 21 and 42 is 42.

Ram and Deepika are running on a circular track. They start at the same time. They take 21 and 42 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 21 and 42 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 21 and 42.
So, LCM of 21 and 42 is 42.

Find the LCM of 21 and 42 using GCF method.

Greatest common factor or gcf of 21 and 42 is GCF(21, 42) x LCM(21, 42) = (21 x 42) / GCF(21, 42) = 42.

Find the least common multiple of 21 and 42.

Least common multiple of 21 and 42 is 42.

Find the least number which is exactly divisible by 21 and 42.

Least number which is exactly divisible by 21 and 42 is 42.