Factors, LCM and HCF or GCD

Factors
2a²bc has 2,a,b and c as factors. Factors are used to find the L.C.M. and H.C.F. of expressions. L.C.M. and H.C.F. also play an important role in mathematics. Suppose you are given some sticks of different sizes and you are asked to find a length whose length will be divisible by all the sticks of different sizes. You need the knowledge of L.C.M. Again consider you are given many sticks and you are asked to find a length which will measure all of them in integer terms. You will need the knowledge of H.C.F.

L.C.M.

Rules to find L.C.M. (Lowest common multiple)

1. Find the L.C.M. of the constant terms.
2. Find the power of all the expressions for each variable or symbolic constant.
3. Find the maximum power for each variable or symbolic constant among each expression.
4. List the variables with the maximum power of each.
5. Multiply it with the L.C.M. of the constant term.

Evaluate L.C.M. of 3a²b⁶c and 8a³b²cd

1. L.C.M. of the constant terms is 24.
2. Power of all the expressions for each variable or symbolic constant.
   a:2 and 3
   b:6 and 2
   c:1 and 1
   d:0 and 1
3. Maximum power for each variable or symbolic constant among each expression.
   a:2 and 3 max = 3
   b:6 and 2 max = 6
   c:1 and 1 max = 1
   d:0 and 1 max = 1
4. List the variables with the maximum power of each.
   a³b⁶cd
5. Multiply it with the L.C.M. of the constant term.
   24a³b⁶cd

L.C.M. is 24a³b⁶cd

H.C.F. or G.C.D.

Rules to find G.C.D. or H.C.F. (Greatest common Divisor or Highest Common Factor)

1. Find the G.C.D. of the constant terms.
2. Find the power of all the expressions for each variable or symbolic constant.
3. Find the minimum power for each variable or symbolic constant among each expression.
4. List the variables with the minimum power of each.
5. Multiply it with the G.C.D. of the constant term.

Evaluate G.C.D. of 3a²b⁶c and 8a³b²cd

1. G.C.D. of the constant terms is 1.
2. Power of all the expressions for each variable or symbolic constant.
   a:2 and 3
   b:6 and 2
   c:1 and 1
   d:0 and 1
3. Minimum power for each variable or symbolic constant among each expression.
   a:2 and 3 max = 2
   b:6 and 2 max = 2
   c:1 and 1 max = 1
   d:0 and 1 max = 0
4. List the variables with the maximum power of each.
   a²b²cd⁰
5. Multiply it with the G.C.D. of the constant term.
   a²b²c

G.C.D. is a²b²c